Triage Evaluation of Gusset Plates in Steel Truss Bridges

Transcription

1 Triage Evaluation of Gusset Plates in Steel Truss Bridges Aaron W. Olson A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering University of Washington 2010 Program Authorized to Offer Degree: Department of Civil and Environmental Engineering University of Washington Graduate School i

2 This is to certify that I have examined this copy of a master s thesis by Aaron W. Olson and have found that it is complete and satisfactory in all respects, and that any and all revisions required by the final examining committee have been made. Committee Members: Jeffrey W. Berman Charles W. Roeder Dawn E. Lehman Date:.. ii

3 In presenting this thesis in partial fulfillment of the requirements for a master s degree at the University of Washington, I agree that the Library shall make its copies freely available for inspection. I further agree that extensive copying of this thesis is allowable for scholarly purposes, consistent with fair use as prescribed in the U.S. Copyright Law. Any other reproduction for any purposes or by any means shall not be allowed without my written permission. Signature: Date: iii

4 University of Washington Abstract Triage Evaluation of Gusset Plates in Steel Truss Bridges Aaron W. Olson Chair of Supervisory Committee: Professor Jeffrey W. Berman Department of Civil and Environmental Engineering The collapse of the I-35W Mississippi River Bridge in Minneapolis, Minnesota in August 2007 called into question the safety of steel truss bridge gusset plate connections. Research into the cause of the failure indicates that several of the gusset plates in the bridge were significantly overstressed at the time of collapse (Ocel and Wright 2008). Based on these findings, the Federal Highway Administration (FHWA) has recommended that these gusset plate connections be load rated using their recommended procedures; a task which had not been required previously. This load rating procedure is complex and would certainly require a significant commitment of resources for the bridges owners, namely state Departments of Transportation. Furthermore, these procedures use the ultimate capacity of the gusset plates and therefore do not address serviceability or bridge longevity; issues which may be better characterized with the prediction of gusset plate yielding, not collapse. A Triage Evaluation Procedure (TEP) is proposed to enable rapid, yet conservative, identification of gusset plates that may be yielding under service loads while eliminating those that iv

5 have sufficient capacity from needing further, more sophisticated analysis. To develop the proposed procedure and evaluate the current FHWA recommendations, detailed non-linear finite element models were created of several gusset plate connections in the Washington State truss bridge inventory along with the critical joint from the I-35W Bridge. Gusset plate behaviors, including yielding and buckling, were studied and the interactions of stresses generated from the loads in the truss elements are considered in the proposed procedure. The Triage Evaluation Procedure is based mechanics and conservative assumptions, which allows for the more rapid evaluation and identification of problem gusset plates while remaining reasonably conservative. This method was then applied to three bridges from the WSDOT inventory, from which 3 of the 35 gusset plates evaluated are identified as needing further investigation. v

6 Acknowledgments The author would like to take this opportunity to acknowledge a few people and institutions for making this research and corresponding thesis possible. First and foremost, this research would not have been possible without the support of professors Jeffrey Berman, Charles Roeder and Dawn Lehman. Their guidance and willingness to help was paramount in the success of this innovative project. The author would also like to thank fellow graduate students Bo-Shiaun Wang ( 王博玄 ) for his support in the analysis of the finite element models, as well as Todd Janes, Olafur Haraldsson, Golnaz Jankhah and Anatalia Countiss for their ongoing advice. The author would like to acknowledge the faculty and staff at the Department of Civil and Environmental Engineering for their hard work in providing an excellent program. This research would not have been possible without the financial support of the Washington State Department of Transportation, Federal Highway Administration and TransNow. On a more personal note, the author would like to express thanks to his teachers and mentors for imparting on him the knowledge that was necessary to be successful in life and graduate school. Also, the author would like to thank his girlfriend, Kristin Auslander and his parents, Cheryl and Gary Myre and Winston Olson, for their ongoing love and support. vi

7 Table of Contents List of Figures... vi List of Tables... xiii Chapter 1: Introduction Statement of Problem Objectives Scope of Work Organization of Thesis... 3 Chapter 2: Review of Recent Literature and Current Evaluation Procedures General Gusset Plate Literature Review Whitmore (1952) Vasarhelyi (1971) Thornton (1984) Yamamoto et al. (1985) Bjorhovde and Chakrabarti (1985) Hardash and Bjorhovde (1985) Brown (1988) i

8 2.10 Yam (1994) Ocel and Wright (2008) Ballarini et al. (2009) Discussion of Previous Gusset Plate Research Rivet Literature Review American Railway Engineering and Maintenance-of-Way Association (1904) Talbot and Moore (1911) Davis, Davis and Woodruff (1939) Wilson, Bruckner and McCrackin (1941) Munse and Cox (1956) Kulak, Fisher and Struik (1987) FHWA Gusset Plate Evaluation Procedures General Resistance of Fasteners Resistance of Gusset Plates Gusset Plate Connections in Tension Gusset Plates Subject To Shear Gusset Plates in Compression FHWA Load Rating Methods Chapter 3: Global Model Development ii

9 3.1 General Model Definitions Description of Bridges Modeled Bridge BR N Bridge BR Bridge BR Bridge Loads Dead Loads Live Loads Model Verification Chapter 4: Gusset Plate Modeling and Observed Behavior used to Develop the TEP General Local Finite Element Model Definitions Joint L2 from BR N Joints L9 and L1 from BR Joints L5 and U3 of BR Joint U10 of I-35W Mississippi River Bridge Gusset Plate Parameters Considered Gusset Plate Yielding Yielding Observations iii

10 4.8.2 Proposed Yielding Check for the TEP Comparison of the TEP Yielding Check with Analytical Results Comparison of Block Shear with the TEP Yield Check Gusset Plate Buckling Buckling Observations Proposed Buckling Check for the TEP Chapter 5: Implementation and Comparison of the TEP with FHWA Procedures General Application of TEP to WSDOT Bridges Comparison with FHWA Load Ratings Load Ratings Including Rivets Chapter 6: Rivet Ultimate Strength and Effective Rivet Yield General Ultimate Rivet Shear Strengths Effective Rivet Yield (ERY) Rivet RF s Using ERY and Revised Ultimate Shear Strengths Effect of Joint Parameters on Rivet Strength Summary Chapter 7: Summary, Conclusions and Recommendations Summary iv

11 7.2 Conclusions Recommendations for Further Research Chapter 8: References Chapter 9: Appendix v

12 List of Figures Figure 2.1: Location of Joint L2 and the prototype used in Whitmore's experiment... 7 Figure 2.2: Effective width determination using the Whitmore method... 8 Figure 2.3: Steel gusset plate specimen and testing apparatus used by Vasarheylyi (1971)... 9 Figure 2.4: Example gusset plate in compression showing L1, L2, L3 and the effective Whitmore width Figure 2.5: Effective length coefficient, K Figure 2.6: Principal dimensions of test specimens and test setup for axial and bending loading Figure 2.7: Shearing stress concentration factors Figure 2.8: Example of gusset plate connection tested by Bjorhovde and Chakrabarti (1985) Figure 2.9: Front and side view of a typical test setup used by Hardash and Bjorhovde (1985) Figure 2.10: Typical block shear failure mode observed by Hardash and Bjorhovde (1985) Figure 2.11: Schematic of test setup used by Brown (1988) Figure 2.12: Gusset dimensions used by Brown (1988) Figure 2.13: Experimental setup of (a) Scheme I, and (b) Scheme II used by Yam (1994) Figure 2.14: Modified Thornton method proposed by Yam (1994) Figure 2.15: Example of test specimens used in AREMA tension test Figure 2.16: Example of rivet shear-joint set plots recorded during AREMA testing Figure 2.17: Example of rivet shear-joint set plots recorded during testing Figure 2.18: Example specimens from the Davis, Davis and Woodruff test program Figure 2.19: Experimental setup used in Munse & Cox test program Figure 2.20: Block shear rupture shear and tension planes vi

13 Figure 2.21: Examples of gross section shear yielding planes Figure 2.22: Examples of net section shear fracture planes Figure 3.1: Examples of built-up truss bridge members Figure 3.2: Example of reduced area of member with hand holes and definition of variables Figure 3.3: Area adjustment coefficient input into SAP Figure 3.4: Photo of BR N Figure 3.5: Schematic of BR N showing joint naming convention and boundary conditions Figure 3.6: Photo of BR Figure 3.7: Schematic of BR showing joint naming convention and boundary conditions Figure 3.8: Sliding pin assembly locations for BR Figure 3.9: Photograph of BR Figure 3.10: Schematic of BR showing joint naming convention and boundary conditions. 49 Figure 3.11: Sliding pin assembly locations for BR Figure 3.12: Schematic of the HS20 Truck load and the HS20 Lane load Figure 3.13: Axial load influence lines for Joint L3 of BR Figure 3.14: Maximum envelope load influence values for HS20 Truck loading of Member L3-L2 on BR Figure 3.15: Position of the HS20 point load and lane load for Member L3-L2 of BR Figure 4.1: Example of 3D finite element model of a truss bridge gusset plate with boundary and loading conditions shown Figure 4.2: Photograph and schematic of Joint L2 from BR N Figure 4.3: Rendering of the finite element model for Joint L2 from BR N Figure 4.4: Photograph and schematic of Joint L9 from BR Figure 4.5: Rendering of the finite element model for Joint L vii

14 Figure 4.6: Photograph and schematic of Joint L1 from BR Figure 4.7: Rendering of the finite element model for Joint L1 from BR Figure 4.8: Photograph and schematic of Joint L5 from BR Figure 4.9: Rendering of the finite element model for Joint L5 from BR Figure 4.10: Photograph and schematic of Joint U3 from BR Figure 4.11: Rendering of the finite element model for Joint U3 from BR Figure 4.12: Photograph and schematic of Joint U10 from I-35W Figure 4.13: Rendering of the finite element model for Joint U10 for I-35W Figure 4.14: Progression of gusset plate with increase in truss member loads. Stress contours show Von Mises stress in ksi. (a) 0% Yielded area, (b) 0.3% Yielded area, (c) 6.5% Yielded area, (d) 10.5% Yielded area and (e) Force in the compression diagonal vs. yielded gusset plate area Figure 4.15: Onset of significant yielding for the gusset plates (a) Joint L2 BR N, (b) Joint L9 of BR 31-36, (c) Joint L5 of BR , and (d) Joint U10 of I-35W Figure 4.16: Depiction of the interference of stresses in the critical area of a typical gusset plate Figure 4.17: Simplified gusset plate geometry used for development of TEP Figure 4.18: Schematic of Joint L5 of BR showing horizontal shear plane passing through hanger member Figure 4.19: Basic connection geometry and definitions Figure 4.20: (a) Block shear failure surface for a chord connection and (b) Whitmore section for a chord connection used for TEP stress calculation Figure 4.21: Ratio of block shear capacity to TEP Yield capacity for chord connections with various connection parameters Figure 4.22: Block shear failure surface for a diagonal or hanger connection and (b) Whitmore section for a diagonal or hanger connection used for TEP stress calculation viii

15 Figure 4.23: Ratio of block shear capacity to TEP yield capacity for diagonal or hanger connections with various connection parameters Figure 4.24: Buckled shapes of (a) Joint L2 of BR N and (b) Joint U10 of I-35W Figure 4.25: Locations where nodal displacements were recorded for gusset plate buckling Figure 4.26: Typical progression of out-of-plane displacement of the gusset plate along the compression diagonal Figure 4.27: Determination of the buckling load using compressive force versus out-of-plane displacement Figure 4.28: (a) Thornton Method for unbraced length, (b) Modified Thornton Method for unbraced length, and (c) Yoo Method for unbraced length Figure 4.29: Comparison of buckling stress versus effective length from analysis with buckling stress predicted using the Thornton method for (a) Joint U10 from I-35W with Fy = 50ksi, (b) Joint L2 from BR N with Fy = 45ksi and, (c) Joint L9 from BR with Fy = 33ksi Figure 4.30: Comparison of buckling stress versus effective length from analysis with buckling stress predicted using the Modified Thornton method for (a) Joint U10 from I-35W with Fy = 50ksi, (b) Joint L2 from BR N with Fy = 45ksi and, (c) Joint L9 from BR with Fy = 33ksi Figure 4.31: Comparison of buckling stress versus effective length from analysis with buckling stress predicted using the Yoo method for (a) Joint U10 from I-35W with Fy = 50ksi, (b) Joint L2 from BR N with Fy = 45ksi and, (c) Joint L9 from BR with Fy = 33ksi Figure 5.1: Joint L3 from BR with (a) RF's calculated using MBE LRFR Service II load combinations under Inventory load levels, and (b) Design drawings of the joint showing milled to bear condition of chord members Figure 5.2: Calculated RF's for Joint U2 of BR using MBE Service II load combinations under inventory load levels and the location of the offset chord splice ix

16 Figure 5.3: ANSYS rendering of the Von Mises stresses for Joint U3 of BR using the MBE LRFR Service II load combination under inventory load levels with chord splice and critical area locations Figure 5.4: Von Mises stress contours for Joint L9 from BR using loads from MBE LRFR rating method and Service II limit state with inventory load level Figure 6.1: Rivet shear stress-joint set plot for a typical riveted joint under axial load that has been divided into four stages Figure 6.2: ERY determined using rivet shear stress-joint set plot Figure 6.3: Example of (a) rivet grip length, and (b) connection length Figure 6.4: Comparison between ultimate rivet shear strength and rivet grip for all tests Figure 6.5: Comparison between ultimate rivet shear strength and rivet grip from AREMA (1904) 131 Figure 6.6: Comparison between ultimate rivet shear strength and rivet grip for Cr-Ni steel from Talbot et al. (1911) Figure 6.7: Comparison between ultimate rivet shear strength and rivet grip for Ni steel from Talbot et al. (1911) Figure 6.8: Comparison between ultimate rivet shear strength and rivet grip from Wilson et al. (1941) Figure 6.9: Comparison between ultimate rivet shear strength and rivet grip for C steel from Davis et al. (1941) Figure 6.10: Comparison between ultimate rivet shear strength and rivet grip for Mn steel from Davis et al. (1941) Figure 6.11: Comparison between ultimate rivet shear strength and connection length for all tests x

17 Figure 6.12: Comparison between ultimate rivet shear strength and connection length from AREMA (1904) Figure 6.13: Comparison between ultimate rivet shear strength and connection length for Cr-Ni steel from Talbot et al. (1911) Figure 6.14: Comparison between ultimate rivet shear strength and connection length for Ni steel from Talbot et al. (1911) Figure 6.15: Comparison between ultimate rivet shear strength and connection length from Wilson et al. (1911) Figure 6.16: Comparison between ultimate rivet shear strength and connection length for C steel from Davis et al. (1939) Figure 6.17: Comparison between ultimate rivet shear strength and connection length for Mn steel from Davis et al. (1939) Figure 6.18: Comparison between ERY strength and rivet grip for all tests Figure 6.19: Comparison between ERY strength and rivet grip from AREMA (1904) Figure 6.20: Comparison between ERY strength and rivet grip for Cr-Ni steel from Talbot et al. (1911) Figure 6.21: Comparison between ERY strength and rivet grip for Ni steel from Talbot et al. (1911) Figure 6.22: Comparison between ERY strength and rivet grip from Wilson et al. (1941) Figure 6.23: Comparison between ERY strength and rivet grip for C steel from Davis et al. (1939). 140 Figure 6.24: Comparison between ERY strength and rivet grip for Mn steel from Davis et al. (1939) Figure 6.25: Comparison between ERY strength and connection length for all tests Figure 6.26: Comparison between ERY strength and connection length from AREMA (1904) xi

18 Figure 6.27: Comparison between ERY strength and connection length for Cr-Ni steel from Talbot et al. (1911) Figure 6.28: Comparison between ERY strength and connection length for Ni steel from Talbot et al. (1911) Figure 6.29: Comparison between ERY strength and connection length from Wilson et al. (1941). 143 Figure 6.30: Comparison between ERY strength and connection length for C steel from Davis et al. (1941) Figure 6.31: Comparison between ERY strength and connection length for Mn steel from Davis et al. (1941) Figure 9.1: First input cells in the TEP spreadsheet Figure 9.2: LL Input and RF Summary Table in the TEP spreadsheet Figure 9.3: Gusset plate property input in the TEP spreadsheet Figure 9.4: Connection information input in the TEP spreadsheet Figure 9.5: TEP yield check in the TEP spreadsheet Figure 9.6: Buckling check in the TEP spreadsheet Figure 9.7: Rivet check in the TEP spreadsheet Figure 9.8: Controlling resistance in the TEP spreadsheet Figure 9.9: Dead and live load factor inputs in the TEP spreadsheet Figure 9.10: Rating factor summary table in the TEP spreadsheet Figure 9.11 Executive summary table in the TEP spreadsheet xii

19 List of Tables Table 2.1: Recommended rivet shear strength values Table 3.1: HS20 Truck load cases for Joint L3 on BR Table 3.2: HS20 Lane load cases for Joint L3 on BR Table 3.3: Comparison of dead loads for BR N Table 3.4: Comparison of dead loads for BR Table 3.5: Comparison of dead loads for BR Table 4.1: Estimated member loads at collapse for Joint U10 of I-35W and the five load distributions used in parametric study Table 4.2: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint L2 of BR N Table 4.3: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint U10 of I-35W Table 4.4: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint L9 of BR Table 4.5: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint L5 of BR Table 4.6: Comparison of the TEP yielding capacity and the predicted buckling load using the Modified Thornton method for Joint L9 of BR Table 5.1: Load factors for load rating with different load rating procedures Table 5.2: Rating Factors for BR N Joints Using the TEP Table 5.3 Rating Factors for BR Joints Using the TEP xiii

20 Table 5.4 Rating Factors for BR Joints Using the TEP Table 5.5: Rating factors for BR N joints from the TEP with Service II Inventory Loads and the FHWA Guide with Strength I Inventory loads Table 5.6 Rating factors for BR Joints from the TEP with Service II Inventory Loads and the FHWA Guide with Strength I Inventory loads Table 5.7 Rating factors for BR Joints from the TEP with Service II Inventory Loads and the FHWA Guide with Strength I Inventory loads Table 5.8: Rivet Shear Strengths as Given by the FHWA Guide Table 5.9 Rating Factors Considering only Rivet Strength for BR N Joints Table 5.10 Rating Factors Considering only Rivet Strength for BR Joints Table 5.11 Rating Factors Considering only Rivet Strength for BR Joints Table 6.1: Summary of ultimate rivet shear strength data Table 6.2: ERY results from rivet tests Table 6.3: Proposed FHWA Guide rivet strength revisions Table 6.4: Rating Factors considering only revised rivet strengths for BR N Joints Table 6.5: Rating Factors considering only revised rivet strengths for BR Joints Table 6.6: Rating Factors considering only revised rivet strengths for BR Joints Table 6.7: Rivet ultimate shear strength calculated for the three WSDOT bridges using rivet test program data of a similar age Table 6.8: Rating Factors considering only rivet strengths based on F u for BR N Joints Table 6.9 Rating Factors considering only rivet strengths based on F u for BR Joints Table 6.10 Rating Factors considering only rivet strengths based on F u for BR Joints Table 6.11: ERY values calculated for the three WSDOT bridges using rivet test program data of a similar age xiv

21 Table 6.12: Rating factors considering only rivet strengths based on ERY for BR N Joints Table 6.13: Rating Factors considering only rivet strengths based on ERY for BR N Joints Table 6.14: Rating Factors considering only rivet strengths based on ERY for BR Joints xv

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23 Chapter 1: Introduction 1.1 Statement of Problem Following the collapse of the steel truss I-35W Mississippi River Bridge in Minneapolis, Minnesota a Federal Highway Administration (FHWA) report (Ocel and Wright 2008) demonstrated that several of the gusset plates were significantly overstressed and that inelastic buckling of one of the plates may have initiated the bridges failure. With these findings came the urgent need to assess the safety of gusset plates on such bridges across the nation. In response, FHWA released the Load Rating Guidance and Examples for Bolted and Riveted Gusset Plates in Truss Bridges (FHWA Guide, FHWA 2009), in order to provide state Departments of Transportation (DOTs) guidance for evaluating gusset plates in their bridge inventories. In addition to checking the fastener resistance, the guidance document includes four gusset plate checks: compressive buckling, tension yielding and fracture, block shear rupture and shear yielding and fracture. The shear strength check requires that the truss element loads be in equilibrium and so point-in-time loads, denoted concurrent loads herein, must be calculated. The calculation of concurrent loads can be quite time consuming and cumbersome and is often not directly outputted from common bridge analysis or load rating software. While it is essential to evaluate the safety of gusset plates, instances of truss bridge failures in the U.S. are rare which suggests that the number of overstressed gusset plates is small. Therefore, a rapid evaluation procedure that is aptly conservative but that can be efficiently and rapidly applied is needed. This procedure should identify gusset plates that may be overstressed and that require a more detailed examination while reducing the time needed to identify the majority that pose no safety concerns. 1

24 1.2 Objectives The primary objective of this research is to develop a process for the safe, consistent and rapid evaluation of gusset plate connections in steel truss bridges. The methodology will utilize envelope member loads rather than concurrent loads to reduce the number of load cases that need to be considered for each joint and will be applicable in the vast majority of situations. The procedure will also be shown to be conservative relative to the recommendations in the FHWA Guide so that it may be utilized in lieu of those methods. 1.3 Scope of Work The outline of the primary tasks of this research is as follows: Review pertinent previous and on-going research regarding gusset plate behavior along with the FHWA methods for evaluating steel truss bridge gusset plate connections. Model select Washington State Department of Transportation (WSDOT) steel truss bridges and select joints from those bridges to study in detail with the purpose of developing the rapid gusset plate evaluation procedure. Develop detailed finite element models of the selected joints to study their general behavior including the onset of gusset plate yielding and compressive buckling. The impact of parameters such as joint geometry, gusset plate thickness and connected member load distributions will be studied using these detailed models. Develop a rapid evaluation procedure, denoted as the triage evaluation procedure (TEP) herein, which is based on simple mechanics and observed behavior from the simulations. Both checks for gusset plate yielding and gusset plate buckling are included. Use the detailed finite element models to compare the ability of the TEP and the methods in the FHWA Guide to predict the onset of gusset plate yielding. 2

25 Use the TEP to load rate three WSDOT bridges to demonstrate that it is conservative relative to the methods in the FHWA Guide while ensuring that it is not overly conservative. Load rate the same bridges considering only the rivet limit state to examine the conservativeness of the recommended rivet strengths in the FHWA Guide. Review previous studies regarding rivet yield and ultimate strengths in order to compare them with the FHWA Guide values. Formulate conclusions and recommendations for further research. 1.4 Organization of Thesis Chapter 2 reviews the pertinent research regarding gusset plate behavior as well as the evaluation procedures contained in the FHWA Guide. Chapter 3 discusses the development and validation of the three global truss bridge models that were developed in order to select and the bridge joints that were used in the detailed analyses. Additionally, there is a description of the live loads that were extracted from the global models which were used in the load rating process. Chapter 4 briefly discusses the development and validation of the detailed finite element analyses of the selected joints. Detailed descriptions of each of the joints selected are provided. Chapter 5 discusses the observed gusset plate behavior during the detailed finite element analyses as well as the derivation of the yielding and buckling checks of the TEP. A comparison between the TEP yield check and the block shear limit state in the FHWA Guide is also made. Chapter 6 presents results from the application of the TEP in the context of several load rating methods. These load ratings are compared to load ratings performed using the methods in the 3

26 FHWA guide. Additionally, load ratings are performed considering only the rivet limit state and the conservativeness of the recommended rivet strengths is assessed. Chapter 7 reviews past research regarding rivet yield and ultimate strengths with the purpose of comparing them to the FHWA Guide recommendations. Chapter 8 includes a summary of the research, conclusions and recommendations for further research 4

27 Chapter 2: Review of Recent Literature and Current Evaluation Procedures 2.1 General This literature review is divided into three sections. First a brief summary of selected previous research on the behavior of gusset plates in braced frames and truss bridges. Bridge gusset plates vary significantly from those in buildings because: (i) they usually connect multiple diagonal members, (ii) they typically serve as chord splices, (iii) they are subject to fatigue conditions, and (iv) are expected to remain elastic throughout their service life. Some of the reviewed research is aimed at characterizing stress distributions and maximum stress predictions for gusset plates, while others are focused on evaluating various gusset plate failure modes such as buckling and fracture. Following the gusset plate literature review is an examination of past literature regarding the ultimate strength and force-deformation behavior of rivets and riveted joints. The data gathered from these sources is presented later in Chapter Chapter 6:. Following the rivet literature review, the current recommendations for gusset plate evaluations in truss bridges are described. 2.2 Gusset Plate Literature Review The following sections describe previous research on the behavior of gusset plate connections in braced frames and truss bridges. 2.3 Whitmore (1952) Whitmore (1952) tested a single prototype joint from a truss bridge to achieve three primary objectives. The first objective was to determine the general distribution of stress that occurs in a gusset plate connection under load. Once the general distribution was understood, the second objective was to locate the maximum intensity of stress. Third, a convenient method for 5

28 determining the magnitude of the maximum stress was sought for later use in the design of such structures. Whitmore s (1952) test prototype was of a five member truss bridge gusset plate connection. In order to best represent the most common types of gusset plate connections that were found in bridge designs of the era, a prototype of joint L2 of a Warren-type highway truss bridge was built (see Figure 2.1). Several simplifications of the specimen relative to an actual bridge gusset plate connection were made. For example, the chord members were continuous through the connection where a splice would typically be present. Furthermore, due to complications with loading, the vertical hanger was treated as a zero force member. The model, shown in Figure 2.1, was ¼ scale and the materials of the members and the plates were the aluminum alloy 61-ST. Strain gages were placed strategically across the gusset plate and the members were loaded according to the demands that would be placed on a bridge of that type. 6

29 Figure 2.1: Location of Joint L2 and the prototype used in Whitmore's experiment The study resulted in many important findings, including: The location of the maximum tensile stress is at the end of the tension diagonal and the location of the maximum compressive stress is at the end of the compression diagonal. The location of the maximum shear stress is located on a plane slightly below the diagonal members and occurs approximately half way between the ends of the diagonals The assumption that the stresses on a plane through the ends of the diagonals due to bending and shearing that are calculated according to the beam formulas P / A Mc / I and VQ / Ib are erroneous. A more appropriate way of determining the maximum stresses in a gusset plate is to use what is now known as an effective Whitmore section. This is defined as the distance between two lines radiating outward at 30 angles from the first row of fasteners in the 7

30 connection along a line running through the last line of fasteners, as illustrated in Figure 2.2. For some connections, this width may be bounded by the edges of the gusset plate itself. By multiplying this effective width by the thickness of the gusset plate, an effective area is found. Dividing the axial load of the member in question by this effective area gives a conservative approximation of the maximum stress in the gusset plate. Figure 2.2: Effective width determination using the Whitmore method 2.4 Vasarhelyi (1971) Vasarhelyi (1971) tested a single 4-member truss bridge joint to experimentally investigate the stress distributions within a gusset plate connection, thus improving the empirical basis for computational stress analysis. It was presumed that with the stress distributions obtained from the experimental results, the validity of other methods of determining gusset plate stress states (i.e. finite element analysis, photoelastic models) could be established. Vasarhelyi (1971) tested a single joint specimen representing a four member steel gusset plate connection. The specimen was very similar to node L2 of a Warren-type truss, however, the vertical 8

31 member was omitted under the assumption that it is typically lightly loaded relative to the other members. The gusset plate specimen was tested under elastic conditions using the apparatus shown in Figure 2.3. Strain measurements were taken using strain gages, whose layout was dictated by the requirements for adequately describing the stress distribution. Generally, these gages were not spread out in an evenly spaced geometric pattern, but were more concentrated in areas where high stresses were expected. Figure 2.3: Steel gusset plate specimen and testing apparatus used by Vasarheylyi (1971) In addition to the steel gusset plate test, a photoelastic test using a in. thick piece of epoxy plastic representing the gusset model was performed. This specimen was hung in a polariscope and loaded so that the isoclinics could be recorded. From these isoclinics, the stress trajectories were drawn. 9

32 In addition to the experimental program, numerical analyses of the gusset plate connection were performed. The results from these analyses were compared to the results obtained from the experimental tests. Based on the experimental results, Vasarhelyi (1971) found that: Duplication of the loading and functioning of a gusset plate under laboratory conditions requires expensive and cumbersome setups. Large numbers of gages and elaborate instrumentation cannot be avoided and is only worsened when the specimen is scaled down. Instead of reproducing conditions in the laboratory, actual structures should be gaged so that their true behavior can be judged The reduced scale photoelastic test appeared to give the best description of the stress field. Vasarhelyi (1971) indicated that the photoelastic experiments should prove to be useful in the testing of different gusset plate configurations. The numerical analyses performed showed the simplified methods of predicting the maximum stress vary only slightly to the experimental results and that their major differences lie in the locations of these stresses. These analyses also showed that the load transfer pattern from the members into the gusset plate is effectively homogenized by St. Venant s effect; thus the use of complex load distribution patterns does not seem necessary. 2.5 Thornton (1984) Based on analysis and observations from a previous test, Thornton (1984) proposed recommendations for the compression strength of a gusset plate connection. The following expressions were proposed to calculate the gusset plate buckling strength: 10

33 I g L t 12 3 wh n p (2.4.1) A L tn (2.4.2) g wh p r s 2 I g t (2.4.3) A 12 g 2 KL F c y r (2.4.4) s E For 2.25 P P F A (2.4.5) r n y g 0.88Fy Ag For 2.25 Pr Pn (2.4.6) where L wh is the effective Whitmore width, t is the plate thickness and n p is the number of main gusset plates. Lc is the unbraced length of the compression member being considered and is calculated by taking the average of the three lengths L 1, L2, and L 3, defined as follows and shown in Figure 2.4: L2 is the distance from the last row of fasteners of the member to the closest adjacent line of fasteners, measured along the centerline of the member. L1 and L 3 are the distances from each end of the effective Whitmore width to the next adjacent line of fasteners, measured perpendicular to the last row of fasteners of the member under consideration. If the effective Whitmore width happens to cross the next adjacent row of fasteners, then these distances are taken as zero. The effective length factor, K, varies depending on the boundary conditions and the types of sway mechanisms and are those commonly used in compression member design as shown in Figure

34 Figure 2.4: Example gusset plate in compression showing L1, L2, L3 and the effective Whitmore width Figure 2.5: Effective length coefficient, K 2.6 Yamamoto et al. (1985) Yamamoto et al. (1985) tested eight gusseted truss joints, six of which can be seen in Figure 2.6. The main objective of this investigation was to determine the gusset plate stress distributions in two common joint configurations including the location and magnitude of the maximum stress intensity. Then, using these stress distributions and magnitudes, a method for designing gusset plates was sought. The two joint configurations considered were derived from a Pratt type truss connection and a Warren type truss connection. In addition to these different geometry types, these 12

35 connections were also classified by how the loads are transmitted between the chord members. As shown in Figure 2.6, connections either had separate gusset plates (designated as spliced-type connections) or the gusset plates were monolithic extensions of the webs of the chords (designated as monolithic-type connections). Figure 2.6 shows that test specimens P-1, W-1, PW-1 and PW-2 are of the monolithic-type connection and that specimens P-2 and W-2 are of the spliced-type connection. The splice type connection is denoted by separate gusset plates that are lapped and bolted to the web plates of the chord members. This type of connection allows for the stresses in one of the chord members to be directly transmitted to the other chord member with the gusset plate taking only a small portion of the load. The monolithic-type connection is significantly different because the gusset plate is simply an extension of the web plate of the chord members rather than a separate plate lapped onto the exterior of the chords. Because these gusset plates transmit the entirety of the chord member forces, they themselves are subjected to high levels of stress. In both connection types, the chord members were continuous through the connection. Loading conditions applied to the gusset plates were classified into two groups: axial loads and bending moments. The two test setups for the application of the axial loads and bending moments are shown in Figure

36 Figure 2.6: Principal dimensions of test specimens and test setup for axial and bending loading The experimental results were used in conjunction with two-dimensional elasticity solutions to develop design equations for determining the thickness required to resist the stresses induced by axial load and bending moments at the ends of the web members. In addition, methods for determining the magnitudes of the maximum shear and normal stresses were also developed. The required thickness of the gusset plate for transmitting axial forces and bending moments from a web member to the gusset plate for both monolithic-type and spliced-type gusset plates are given as: t P10 be a 1 I 2 A 1 d 3 w w 2 b 2 (2.5.1) 14

37 where t is the gusset plate thickness (in.), P is the axial force in the web member (kip), be is the effective width given by the equation b e b 0. 8d, where b is the connection width (in.), d is the 4 connection width (in.), I w is the moment of inertia of the web member ( in ), Aw is the cross- 2 sectional area of the member ( in ) and a is the allowable stress of the gusset plate material (psi). The required thickness for a gusset plate for transmitting the horizontal shear force due to the web member forces is for spliced-type connections is given as: 310 t 4 4 P R P B a L (2.5.2) where P and P are the forces in the right-hand chord member and the left-hand chord member in R L kips, respectively, B is the gusset plate width (in.) and a is the allowable shearing stress for the material (psi). The Von Mises stress state can be calculated using Equations (2.5.3), (2.5.4) and (2.5.5) o 1. 2 a (2.5.3) PR PL 10 3 (2.5.4) 2Bt P 10 3 R o PR PL (2.5.5) AG AC where A G is the sectional area of the gusset plates, AC is the sectional area of the chord and κ is a stress concentration factor given by the table shown in Figure 2.7, where is the angle of the web i 15

38 member in question with respect to the chord members. The shear stress,, and normal stress, o, are calculated using the forces in the chord members divided by and effective area. Figure 2.7: Shearing stress concentration factors 2.7 Bjorhovde and Chakrabarti (1985) Bjorhovde and Chakrabarti (1985) performed an experimental investigation into the behavior of full scale braced frame gusset plate connections, as shown in Figure 2.8, that were typically used in heavy industrial structures. Six total tests were performed, with three tests at two different plate thicknesses (1/8 in. and 3/8 in.) and three different bracing member orientations (30, 45 and 60, measured from the beam axis). The gusset plate connections were designed initially based on Canadian limit states design criteria for steel structures, using the Whitmore criterion to check the plate capacity. Additionally, net and gross section checks were performed at many different locations around the diagonal connection to the gusset plate. During the test program, strains and displacements of the specimens were recorded as well as the mode of failure. In addition to the test program, several analytical finite element models of the connections were created so that their results could be compared to the results gathered from the experiment. 16

39 Figure 2.8: Example of gusset plate connection tested by Bjorhovde and Chakrabarti (1985) Based on the experimental and analytical results, Bjorhovde and Chakrabarti (1985) found that: For the bracing connections investigated, the primary failure mode of the gusset plate was a tear that occurred across the bottom bolt holes of the splice connection between the gusset plate and the bracing member. Other failure modes observed in the gusset plate occurred when the plate boundaries were intercepted by the Whitmore zone. This was observed in the 60 brace angle connections where the plate failed by tearing at the bolt holes of the double angle that fastened the plate to the column. 17

40 The type and location of the gusset plate boundaries, along with the pattern of load transfer to the plate, have significant secondary effects on plate buckling and associated out-of-plane bending. Gusset plate buckling as a result of secondary effects seems to play a significant role in the design criteria of gusset plates. The use of gusset plate stiffeners should be considered in the design of such connections, however, further studies are recommended. The analytical and experimental results were found to be in reasonable agreement with each other. The findings of the test programs are in satisfactory agreement with the Whitmore concept of designing gusset plates. 2.8 Hardash and Bjorhovde (1985) Hardash and Bjorhovde (1985) performed an experimental investigation into the behavior and ultimate strength of a single member gusset plate in tension. The purpose of the experiment was to develop an improved design method based on an ultimate strength approach. Three separate test programs were developed at the University of Arizona, University of Illinois and the University of Alberta. Single specimens were instrumented to record displacement data and then placed into a Tinius-Olsen universal testing machine, shown in Figure 2.9, and loaded to failure. 18

41 Figure 2.9: Front and side view of a typical test setup used by Hardash and Bjorhovde (1985) The failure mode most commonly observed consisted of tensile failure along the last row of bolts along with elongation of the bolt holes in the direction of the applied load, as shown in Figure Based on the experimental data and observations it was determined that for a tensile gusset plate connection a block-shear model must incorporate two conditions: tensile resistance developed at the last row of bolts and shear resistance developed along the outer bolt lines. 19

42 Figure 2.10: Typical block shear failure mode observed by Hardash and Bjorhovde (1985) Based on the experimental results, Hardash and Bjorhovde (1985) found that: All of the ultimate failure modes observed consisted of tensile tearing along the last row of bolts along with varying degrees of shear yielding occurring at the outer lines of bolts. The governing block-shear model utilized a combination of tensile ultimate stress on the net area between the last row of bolts and a uniform effective shear stress acting along the gross area long the outer bolt lines. 2.9 Brown (1988) Brown (1988) performed an experimental investigation into the behavior of a single plane gusset plate connection loaded in compression with the purpose of developing a rational analytical model which could accurately predict the compressive load carrying capacity of these types of connections. Twenty-four test specimens were fabricated and tested in compression using a Tinius-Olsen Testing Machine, as shown in Figure The behavior of the gusset plate was monitored using strain gages 20

43 to determine stress distributions and dial gages to monitor out-of-plane displacement at various locations. In order to better characterize the behavior of many gusset plate connection types, several different brace angles and plate thicknesses were tested. Figure 2.11: Schematic of test setup used by Brown (1988) Based on the experimental results, Brown (1988) found that: Buckling of the unsupported edges of the gusset plate was the primary failure mode for this type of connection and was initiated at the longer unsupported edge. For a given plate thickness, buckling resistance is inversely proportional to the unsupported edge length, but is also dependent on the geometry of the bracing member-to-gusset connection. For compact gusset plates with small unsupported edge length to thickness ratios, bearing failure modes are also an important consideration. 21

44 Using the experimental data, a rational model for plate buckling capacity was developed and is given as follows. An equivalent slenderness ratio for steel gusset plates can be determined using: KL r equiv 4 t (2.8.1) where α is the unsupported length of the longer free edge and t is the plate thickness. Using this slenderness ratio, an allowable stress, F, is found using Table 3-36 of the American Institute of a Steel Construction Manual of Steel Construction, 8 th ed. The allowable plate load in compression is given by the following equation: Fa 2L tnp a cos 2p esin P (2.8.2) where L is the total gusset length, θ is the angle between the brace and the longer free edge, n is the number of bolt rows in the direction of loading, p is the bolt pitch and e is the edge distance to the centerline of the first bolt row, as shown in Figure

45 Figure 2.12: Gusset dimensions used by Brown (1988) 2.10 Yam (1994) Yam (1994) performed an experimental investigation to determine the compressive behavior and strength of a single member gusset plate connection which are typically found in building braced frames. The test program included thirteen full-scale with varying test parameters such as gusset plate thickness, size and brace angle being considered. Additionally, the effects of frame action on the behavior of gusset plates in compression were investigated. The experiment used two different test setups, as shown in Figure 2.13, denoted as Scheme I and Scheme II. The concept used in Scheme I is that the same out-of-plane displacement mode of the gusset plate can be attained by allowing the column base and beam to sway out of plane instead of the bracing member. Scheme II allows for the bracing member to move out-of-plane when gusset plate buckling occurred. Additionally, Scheme II allowed for the application of beam and column moments. In both schemes, the gusset plates were instrumented such that strains and out-of-plane displacements could be recorded. 23

46 Figure 2.13: Experimental setup of (a) Scheme I, and (b) Scheme II used by Yam (1994) In addition to the experimental program, numerical analyses of the gusset plate connections were created using the finite element program ABAQUS. The results from these analyses were then compared to those retrieved from the experimental program. Based on the experimental and analytical results, Yam (1994) found that: Of the specimens tested, the failure mode of the gusset plates was sway buckling. In general, the gusset plate underwent significant yielding prior to them reaching their ultimate loads, except for the slender specimens. The ultimate loads of the specimens proved to increase nearly linearly proportional to the gusset plate thickness. The finite element models proved to simulate the ultimate strength and behavior of the test connections quite well. The Whitmore method proved to be a conservative estimate of the ultimate strength of the compact specimens. However, this method underestimated the ultimate strength of the more slender specimens. 24

47 The Thornton method provided conservative estimates of ultimate strength of the specimens tested. The Modified Thornton method, which uses a 45 dispersion angle rather than the 30 angle proposed by Thornton and the centroidal unsupported length, L 2, as shown in Figure 2.14, offers a good prediction of the ultimate buckling strength of a gusset plate connection. Figure 2.14: Modified Thornton method proposed by Yam (1994) 2.11 Ocel and Wright (2008) Ocel and Wright (2008) performed and analytical investigation to determine the contributing factors that may have led to the collapse of the I-35W truss bridge in Minneapolis, Minnesota on August 1, For this investigation, seven separate global models of the I-35W Bridge were created to explore the different aspects of the bridge failure. These global models were built using ABAQUS versions 6.6 and 6.7 software and were used to study the structural response of the bridge under a multitude of different loading conditions. Once the global response of the bridge was well understood, a more detailed, localized model of Joints U10W, U10E, L11E and L11W was embedded into the global models. These local models were constructed using meshed shell elements representing the members and the gusset plate in the local area of the connection. Rivet holes and rivets were not modeled explicitly, however, in the rivet locations the members and the gusset 25

48 plates were linked to one another using a multi-point nodal constraint that locks all degrees of freedom together. No attempts to model fracture of any steel components or rivets were made. The following is a list of the relevant findings of this study: The gusset plates located at Joints U10 and L11 were undersized for both the original design forces and the forces present at the time of collapse. At the completion of construction in 1967, the gusset plate region located at the end of the compression diagonal in joint U10 likely had stresses exceeding the yield stress of the plate material. The size of the yielded area was increased significantly after roadway modifications were made in the late 1990 s and increased even further with the presence of construction/traffic loads present at the time of collapse. The failure mode that was predicted by the detailed local model was inelastic buckling of the gusset plates located at the end of the compression diagonal at Joint U10. The critical buckling load was impacted significantly by the presence of initial gusset plate imperfections that were observed during previous bridge maintenance inspections. When the detailed model of Joint U10 was taken past the point of the aforementioned critical buckling load, tensile fracture of the gusset plate would have likely occurred prior to achieving post-buckling equilibrium. Thus, it was postulated that buckling of the U10 gusset plate led to a set of circumstances involving large deformations and tensile rupture of the gusset plate ultimately leading to the failure of the bridge Ballarini et al. (2009) Ballarini et al. (2009) performed an analytical investigation to explore the stress and strain conditions that may have lead to the failure of the Joint U10 gusset plate from the I-35W Bridge in Minneapolis, MN using detailed finite element analyses. For this investigation, finite element models 26

49 were used at the global and local levels to help determine the possible stress states of the gusset plates at Joint U10. This particular gusset plate had been previously identified by an investigation led by the National Transportation Safety Board (NTSB) as playing a key role in the sudden collapse of the bridge (Ocel and Wright, 2008). A 2D model of the bridge was created using SAP2000 in order to study the global response of the bridge. Once the forces in each member of the truss were determined from the global analysis, a detailed 3D finite element model of the Joint U10 using ABAQUS was generated. This model used eight-node, isoparametric brick elements throughout the structure. Rivets were modeled as rigid cylindrical shells and contact was used to model their interaction with the edges of their respective holes. The key findings of this investigation are summarized as follows: A significant portion of the U10 gusset plates may have yielded at the time of the bridge collapse. The interaction of compression and shear may have been a key factor in the gusset plate failure, however, this interaction is not well understood and further study is recommended Discussion of Previous Gusset Plate Research Insert discussion here Rivet Literature Review The following sections describe previous research regarding the ultimate strength and forcedeformation behavior of rivets and riveted joints. 27

50 2.15 American Railway Engineering and Maintenance-of-Way Association (1904) The American Railway Engineering and Maintenance-of-Way Association (AREMA 1904) tested many riveted joints of various configurations. This section summarizes the testing program, results and conclusions. In this test program, 90 separate lap splice connections were tested with connection elements tension and varying number of rivet shear planes. Five specimens were produced for each of the eighteen different joint configurations which varied in from single rivet joint to joints with multiple rivets and layered fill plates. Examples of the simplest and most complex joints are shown in Figure Both the rivet and plate material was specified as Open-Hearth (OH) steel and multiple coupon tests of the material were performed to give the necessary material properties. As the joints were loaded in tension, force-deformation data points were recorded at regular intervals. Joint deformation was recorded as what is called joint set, which is described as the permanent deformation of the joint. Joint set is measured using micrometer-extensometers attached to the edges of the main plates just beyond the splice plates. The specimen is loaded to 1000 lbs. and the micrometer reading is recorded. The specimen is then loaded to the desired load for a particular load step and then unloaded to 1000 lbs. again. The micrometer is read again and the difference between the initial micrometer reading and the reading is called the joint set. Each test consisted of at least 14 load steps. The load was converted into an average rivet shear stress by dividing the total load by the total cross sectional area of the undriven rivets. For each specimen a plot, an example of which is shown in Figure 2.16, was created showing the relationship between the average rivet shear stress and the joint set. Additionally, the maximum load for the joint was recorded as well as a brief description of the failure mechanism. It should be noted that the force-deformation data for 28

51 each joint was only recorded up to a certain point. That is, deformations were only recorded to approximately 75% of the ultimate strength of the joint. After that, only the ultimate strength of the joint was given with no accompanying displacement data. Ultimate rivet strengths obtained from this research are presented in Section 6.2. Figure 2.15: Example of test specimens used in AREMA tension test Figure 2.16: Example of rivet shear-joint set plots recorded during AREMA testing In addition to providing a great deal of data on the behavior of riveted joints, including ultimate rivet strengths and joint force-displacement relationships, the authors drew a number of conclusions that are pertinent to the current research including: 29

52 Resistance of a riveted joint against shearing forces, up to the yield point, is due to the friction between the surfaces of the plates held in contact by the rivets The yield point of a riveted joint is reached when the shearing forces are equal to the frictional forces. After the yield point has been reached and the joint slips, the rivets come into bearing against the edge of the rivet hole. At that point a deformation of the body of the rivet begins with an accelerating increase in the resistance until the entire side of the body of the rivet comes into contact with the edge of the rivet hole. Beyond this point, the deformation continues with a decrease in stiffness until the ultimate strength of the rivet is reached and failure of the joint occurs. A riveted joint that is subjected to forces always in the same direction can safely be strained beyond the yield point, up until the point where the rivets come fully into bear against the edge of the rivet holes Talbot and Moore (1911) Talbot et al. (1911) tested joints that were identical to the AREMA tests in 1904 except that different rivet and plate materials were used. Ninety tests using Nickel-steel rivets were performed along with 54 tests using Chrome-Nickel-steel rivets. Both force-joint set plots and ultimate rivet shear stresses for each joint were recorded. Coupon tests of the materials were also performed in order to provide the necessary material properties. Figure 2.17 shows an example rivet shear-joint set plot from the test program. 30

53 Figure 2.17: Example of rivet shear-joint set plots recorded during testing Similar to the AREMA tests, this test program generated a considerable amount of data regarding the force-displacement and ultimate strengths of the riveted joints. Additionally, the conclusions that the authors reached are listed as follows: The experimental evidence indicates that the resistance of the joint to first noticeable slip of the rivet depends more on the workmanship involved in properly preparing the rivet hole, rather than the rivet material itself. In riveted joints that are designed on the basis of ultimate strength, ultimate strength of the rivet and plate material is of utmost importance and thus the use of special steels may be warranted. In riveted joints that are designed on the basis of the frictional hold of rivets, ultimate strength of the rivet material is less important because initial slip of the joint occurs at the same point between high strength steel and ordinary steel. 31

54 2.17 Davis, Davis and Woodruff (1939) Davis et al. (1939) experimentally investigated the behavior of large riveted joints under static tension. The effect of using different rivet and plate steels on the behavior of the joint was also investigated. In this test program 37 different joint configurations were tested which varied in the number of rivets as well as the number of plates in each connection. An example of the smallest and largest joints tested is shown in Figure Along with reporting ultimate rivet shear stresses, this paper also introduced the concept of Effective Rivet Yield (ERY) which is discussed later in this chapter. Figure 2.18: Example specimens from the Davis, Davis and Woodruff test program In addition providing data on ultimate rivet strengths and ERY, the following is a list of conclusions relevant to the current research that were reached by the authors: There is no justification for the use of elaborate formulas to calculate the effect of rivet stagger on the net section The practice of assuming that equal shear per rivet, regardless of the length of the joint, is satisfactory 32

55 2.18 Wilson, Bruckner and McCrackin (1941) Wilson et al. (1941) tested three individual specimens of seven different lap splice joint configurations in tension using three different low-alloy steels resulting in a total of 63 distinct tests. The three alloys were created in accordance with ASTM Tentative Specifications A242-41T. The main purpose of these tests was to determine the behavior of these joints fabricated with these steels. Tests were performed to determine the following: tensile strength of the material, shearing strength of driven rivets and material hardness. In addition to these items, force-displacement plots were recorded for each specimen. These test provided a considerable amount of force-deformation data for riveted joints as well as ultimate rive shearing strength. These were the only items that were utilized from this report Munse and Cox (1956) Munse et al. (1956) investigated the behavior of rivets in tension, shear and combined tension and shear. The testing program outlined in this paper differed from the previous tests in that the strengths of individual rivets were investigated. A single rivet was placed into an apparatus which was able to test the strength of the rivet under different combinations of tension and shear, as shown in Figure The data collected from these test and used later come from the 44 tests with rivets loaded only in shear. Munse et al. (1956) reported only ultimate rivet shear strengths; no force-displacement relationships were provided. 33

56 Figure 2.19: Experimental setup used in Munse & Cox test program Aside from the significant amount of data regarding ultimate shear strength of rivets, the following conclusions were reached by the authors: The method of rivet manufacturing (hot or cold formed) had very little effect on the ultimate strength of the rivet. The energy absorbing capacity of rivets subject to static loads is greatly reduced with increasing shear-tension ratios Kulak, Fisher and Struik (1987) Fisher et al. (1987) developed design guidance for bolted and riveted joints based on previous experimental data. The ratio of the shear strength, u, to the tensile strength, u, of a of a rivet was proposed to be unrelated to rivet grade, installation procedure, diameter and grip length. Testing showed that the relationship between these strengths is reasonably given by: 34

57 0. 75 (2.17.1) u u The shear resistance of a rivet is directly proportional to the shear area and number of shear planes and so the shear resistance, S, of a rivet is given by: u S 0.75 (2.17.2) u ma b u where m is the number of shear planes and A b is the cross-sectional area of the undriven rivet FHWA Gusset Plate Evaluation Procedures General In response to the collapse of the I-35W bridge, several investigations have concluded that one or more gusset plates on the bridge were significantly overstressed (Ocel and Wright 2008 and Ballarini et al. 2009). Following these findings, the FHWA directed all state DOT s to immediately begin evaluating the load carrying capacity of truss bridge gusset plates; a task which had never been required previously. To assist in these evaluations the Load Rating Guidance and Examples for Bolted and Riveted Gusset Plates in Truss Bridges (FHWA 2009) was released which included four primary plate checks as well as checks for fastener resistance. Once the appropriate governing resistances for the gusset plate are determined, the gusset is load rated using the rating factor (RF) method. The following sections describe the design checks and load rating techniques given in the design guidance document Resistance of Fasteners For axially loaded members connected with concentrically loaded bolted and riveted gusset connections it is assumed that the load is distributed equally to all fasteners. 35

58 For bolted gusset plate connections, the bolts shall be evaluated for bolt shear and the plate shall be evaluated for bearing failures at the strength limit state. At this limit state, the AASHTO LRFD Articles and shall apply for determining the appropriate resistance to prevent bolt shear and plate bearing failures. Similarly, riveted gusset plate connections need to be evaluated for rivet shear and plate bearing failures at the strength limit states. The plate bearing resistance is determined using the same AASHTO Article The factored shear resistance of a single rivet is given as: R FmA r (2.18.1) where m is the number of shear planes, F Ar is the cross-sectional area of the rivet before driving and is the factored shear strength of one rivet. Rivet shear strengths are given in Table 2.1 and are based on an ASTM designation or the year of construction for rivets of unknown origin. Table 2.1: Recommended rivet shear strength values Year of Construction F (ksi) Constructed prior to 1936 or of unknown origin 18 Constructed after 1936 but of unknown origin 21 ASTM A 502 Grade I 27 ASTM A 502 Grade II 32 For riveted connections longer than 50 inches, the shear resistance of the rivets is taken as 0.80 times the values of the value given in Equation (2.18.1). The length of the connection is measured as the distance between the extreme rivets on one side of the connection to the other. 36

59 Resistance of Gusset Plates Gusset plates with multiple members attached may have regions of tension, compression and shear that must be evaluated to find the limiting gusset plate strength. The limit states recommended in the FHWA Guide for each gusset plate loading are briefly described below Gusset Plate Connections in Tension Gusset plate connections in tension are to be checked for the following three conditions: Yielding over the gross Whitmore section Fracture on the net Whitmore section, and Block shear rupture The factored resistance, P, is to be taken as the smallest strength from these limit states. Gross section yielding resistance is given by: r P r P F A (2.18.2) y nu y y g where is the resistance factor for yielding, which in this case is taken as 0.90, F is the yield y y strength of the plates and A g is the gross cross-sectional area of the plates. For determination of the gross cross-sectional area, the effective gross width of the gusset plate in tension is determined using the Whitmore width method, as described previously. In cases where the chord members of the truss framing into the gusset plate are in tension there may be additional plates, such as splice plates and wind bracing gusset plates, which work in concert with the main gusset plate to transfer load. These additional areas must also be included using the Whitmore effective width method. Once the all the pertinent effective widths are determined, they are multiplied by their respective plate thicknesses and summed to give the total gross cross-sectional area, A g. After gross section yielding resistance is determined, net section fracture resistance is given as: 37

60 P r P F A U (2.18.3) u nu u u n where u is the resistance factor associated with tension fracture, which in this case is taken as 0.85, Fu is the tensile strength of the plates and A n is the net cross-sectional area of the plates. The shear lag reduction factor, U, is taken as 1.0 for gusset plates. The net cross-sectional area is the gross cross-sectional area reduced according to the loss of section associated with fastener holes along the effective Whitmore width. Block shear rupture resistance is the achieved by the combination of resistances associated with parallel and perpendicular planes; one in tension and the other in shear. The factored block shear resistance is given by: If A 0. 58A tn, then P 0. 58F A F A vn r (2.18.4) bs y vg u tn Otherwise P 0. 58F A F A r (2.18.5) bs u vn y tg where is the resistance factor associated with block shear, which in this case is taken as 0.80 and bs F and F are the yield strength and tensile strength of the plates respectively. Block shear rupture y u analysis involves examining multiple combinations of yielding and rupture planes to find the combination that gives the least resistance. Figure 2.20 illustrates planes in the gusset plate that resist shear and tension stresses along the connection of the members loaded in tension. The first combination of failure planes that is checked is given in Equation (2.18.4) and is a combination of gross area yielding along the planes resisting shear stress and net section fracture along the planes resisting tension. The second combination of failure planes that is checked is given in Equation (2.18.5) and is a combination of net section fracture along the planes resisting shear and gross area yielding along the planes resisting tension. The difference between the net and gross cross-sectional 38

61 areas for the tension and/or the shear areas is that the net area accounts for loss of section due to holes for fasteners while the gross area does not. Figure 2.20: Block shear rupture shear and tension planes Gusset Plates Subject To Shear The factored shear resistance for a gusset plate, V, is given by the lesser of the shear yield resistance given by Equation (2.18.6) or the net section shear fracture resistance given by Equation (2.18.7). r V V 0. 58F A (2.18.6) r vy n vy y g V V 0. 58F A (2.18.7) r vu n vu u n The resistance factors and are the resistance factors associated with shear yielding and shear vy vu rupture and are taken as 0.95 and 0.80, respectively. The gross and net areas of the plates that resist shear are denoted A g and A n, respectively. The reduction factor, Ω, has two possible values. It is taken as 1.0 when the gusset plate is of ample stiffness to prevent buckling and develop the plastic shear force of the plates. In the absence of more rigorous analysis or conditions that assure that the 39

62 full plastic shear capacity of the plates can be achieved, this reduction factor is to be taken as Analysis of the shear capacity of the gusset plate requires that several critical shear sections be examined and that the section that provides the least resistance will govern. Examples of a gross area sections and net area sections can be seen in Figure 2.21 and Figure 2.22, respectively. Figure 2.21: Examples of gross section shear yielding planes Figure 2.22: Examples of net section shear fracture planes 40

63 Gusset Plates in Compression Analysis of gusset plates in compression is highly dependent on the geometry of the plate, the boundary conditions and the current state of stress the plate is under. These conditions are integral in determining the correct compressive resistance and buckled shape of a gusset plate in compression. In lieu of a more rigorous analysis, the FHWA Guide recommends the compression resistance be determined via the column buckling analogy which is given in AASHTO LRFD Articles and by Equations , and FHWA Load Rating Methods Once the appropriate resistance for each member in the gusset plate has been determined, the next step is to determine the governing rating factor for the gusset plate. Load rating is a procedure whereby the safe live load carrying capacity of the gusset plate is determined under various loading conditions. Load rating is quantified using the RF, which is a form of a capacity-to-demand ratio and is calculated per the 2008 AASHTO Manual for Bridge Evaluation (MBE, AASHTO 2008) using: RF C cdc wdw LL I L (2.18.8) where C is the governing capacity of the connection under consideration (i.e. the controlling resistance determined previously). The terms DC and DW are the demands for the connection attributed to the dead loads caused by the bridge components and the roadway wearing surfaces, respectively. The load factors c, w and L are the load factors for the bridge components, roadway wearing surfaces and live loads, respectively. The term LL is the demand due to the live loads on the bridge and I is the impact factor associated with the live loads. The load factors are dependent on the type of load rating being performed and may be found in Table 6A of the MBE. 41

64 Bridges are generally rated for at least two main rating levels, denoted as the Inventory and Operating Rating Levels. Inventory rating is a capacity rating which results in loads that the structure can safely carry for an indefinite amount of time. Operating rating results in the absolute maximum permissible load that the structure can carry corresponding to the vehicle used in the rating. This load level is intended to only occasionally be reached during the bridges lifetime considering that repeated loading of this type may significantly decrease the life of the structure. A rating factor is calculated for each connection on the gusset plate for the different load rating levels and the lowest RF value is the governing value for that particular gusset plate. 42

65 Chapter 3: Global Model Development 3.1 General This section discusses the development of global bridge models which were used to determine member loads in three Washington state truss bridges. Member loads were then used to identify joints having gusset plates with relatively high stresses and to establish loading for the detailed analyses. 3.2 Model Definitions Each bridge was modeled using a linear-elastic analysis using the structural analysis package SAP2000. None of the bridges considered were skewed or curved, thus, it was determined that they could be effectively modeled as a two dimensional, plane truss. The first step in modeling each bridge was to determine the pertinent section properties, such as cross-sectional area and moment of inertia, using the shop and design drawings for each bridge provided by the Washington State Department of Transportation (WSDOT). Members were often constructed as built-up sections with combinations of channels, angles and/or plates fastened together with rivets. It was assumed that the rivets were sufficiently stiff enough to ensure that the member behaved as a single section. Examples of common built-up sections are shown in Figure 3.1. Figure 3.1: Examples of built-up truss bridge members 43

66 Some built-up sections ended up as closed rectangular elements and so hand holes were spaced at regular intervals to provide access for maintenance, as shown in Figure 3.2. The presence of these hand holes made it necessary to reduce the cross-sectional area of the member based on the number of hand holes along its length. This was done by calculating an area adjustment coefficient, η, based on the length of the member and the number and size of the hand holes. This area adjustment coefficient is calculated using the following equations: (3.2.1) (3.2.2) (3.2.3) Figure 3.2: Example of reduced area of member with hand holes and definition of variables Where is the gross cross-sectional area, is the number of hand holes along one side of the member, and is the area of the hand hole. All other terms in these equations are defined in Figure 3.2. Once this area adjustment coefficient had been determined, it was used as a frame property modifier in SAP2000, which effectively reduces the gross cross-sectional area of each member during the analysis. Figure 3.3 shows the dialog box in SAP2000 where the area adjustment coefficient is inputted. 44

67 Figure 3.3: Area adjustment coefficient input into SAP2000 Once the appropriate sections properties were determined, models of each bridge were created using the predefined frame elements in SAP2000. Member lengths were taken directly from the drawings and are the distances between the work points for each gusset plate connection. As is common when analyzing truss structures, members were modeled as having only axial forces. This was done by utilizing moment releases at each end of the member. For the sake of comparison, the bridges were also modeled without the moment releases and the differences in axial loads and the magnitudes of the induced moments proved to be negligible. 3.3 Description of Bridges Modeled The following sections describe the three bridges that were modeled from the WSDOT bridge inventory Bridge BR N Bridge BR N is a 220 ft. long, single span through truss bridge built in 1949 that carries two lanes of traffic; a photo of which can be seen in Figure 3.4. Figure 3.5 shows the naming convention used for each of the nodes on the bridge. At the support node L0, the design drawings show a pinned support and at node L8 there is a roller support. The pin support allows for free rotation of the node, but restrains the horizontal and vertical movement. The roller support allows for free 45

68 rotation, as well as vertical and horizontal translation. These boundary conditions were included in the global analysis and can be seen in Figure 3.5. It should be noted that no field verification of the conditions of these supports was made. Figure 3.4: Photo of BR N Figure 3.5: Schematic of BR N showing joint naming convention and boundary conditions Along the lower chords of the two identical trusses span floor beams which support the bridge deck and vehicular traffic. These floor beams frame directly into the nodes of the main bridge trusses allowing for the dead and live loads from the bridge deck to be modeled as point loads at the bridge panel points. Along the top chord of the truss, wind bracing frames into the panel points and so dead loads associated with these members are modeled as point loads at the nodes. 46

69 3.3.2 Bridge BR Bridge BR is an under-slung truss bridge built in 1950 that has a cantilever span that supports a simple drop-in span in the middle. The bridge is 524 ft. long and has two main support piers approximately 142 ft. from each end of the bridge, as seen in Figure 3.6. Figure 3.7 shows the naming convention for the nodes; however, in the interest of space only half of the bridge is shown. Figure 3.6: Photo of BR Figure 3.7: Schematic of BR showing joint naming convention and boundary conditions After examining the design drawings a pin support was assigned to node L7 and a roller support was assigned to node L0. Boundary conditions for this bridge were assumed to be symmetric, so similar support conditions were assigned to the corresponding nodes on the remaining half of the bridge. Because of the drop-in span in the middle of the bridge, there is a need for expansion joints between the cantilever portion of the bridge and the simply supported portion. This is 47

70 accommodated by having sliding pin assemblies between nodes U10-U11 and nodes L9-L10, shown in Figure 3.8. These pin assemblies allow for free motion in the direction of the members connecting the two nodes, thus effectively making them zero-force members. To model these sliding pin assemblies, axial force releases were assigned at the ends of the frame members where each assembly is located. Figure 3.8: Sliding pin assembly locations for BR The roadway on BR is carried by floor beams that span across the two top chords of the identical main bridge trusses. These floor beams come to rest directly at the top of the chord at each panel point and so dead and live loads attributed to the road deck are modeled as point loads at the nodes. Dead loads associated with wind bracing and other structural elements that come to rest along the bottom chord are also modeled as point loads at their corresponding nodes Bridge BR Similar to BR 31-36, BR is an under-slung truss bridge built in 1930 that has a cantilever span that supports a simple drop-in span in the middle. It is 392 ft. long with two main support piers 48

71 approximately 71 ft. from each end of the bridge. Figure 3.9 shows a photograph of the bridge and Figure 3.10 is a schematic showing the naming convention for the nodes along the bridge. Only half of the bridge is shown due to space constraints and the fact that the bridge is symmetric about the center of the span. Figure 3.9: Photograph of BR Figure 3.10: Schematic of BR showing joint naming convention and boundary conditions After examining the design drawings, a pin support was assigned to node L4 and a roller support was assigned to node U0. Boundary conditions were assumed to be symmetric, so similar support types were assigned to the support nodes for the other half of the bridge. Similar to BR 31-36, BR has a drop-in simple span that requires the need for an expansion joint which is accommodated by 49

72 similar sliding pin assemblies. These assemblies are located on the members spanning between nodes L8-L9 and U9-U10 and are shown in Figure Figure 3.11: Sliding pin assembly locations for BR Sliding pins result in Members L8-L9 and U9-U10 being zero-force members and are modeled as such by having axial load releases at their ends where the pin assemblies are located. Loads from the road deck are transferred from floor beams spanning between the main trusses to the panel points along the top chord. These loads are modeled as point loads at the bridge nodes. Dead loads along the bottom chord attributed to wind bracing or other structural members are also modeled as point loads at the nodes. 3.4 Bridge Loads In order to perform further analysis of the gusset plates and carry out the load rating procedure, the dead and live loads for each bridge had to be determined. Dead loads are loads attributed to the self weight of the structure and the roadway it supports. Live loads are loads attributed to vehicular 50

73 traffic crossing the bridge. The following sections describe the processes used to determine these loads Dead Loads In order to determine the appropriate dead loads to input into the bridge model, design drawings for the bridges were carefully examined. The road deck on all three bridges considered is carried by floor beams spanning transverse to the main bridge trusses; therefore, the tributary area method was used to distribute the loads from the road deck to the floor beams. The reactions from the floor beams were then applied as point loads to the truss nodes. Similarly, loads from the wind bracing and other structural elements were also distributed to their appropriate nodes. Unit weights for the structural steel and concrete used in the dead load determination were 490 lb ft 3 and 150 ft 3 respectively. In addition to the road deck shown in the design drawings, WSDOT recommended adding a 4 in. thick layer of latex modified concrete as a wearing surface. lb, Live Loads The live loads for each bridge correspond to the HS20 Truck and HS20 Lane load as described in Chapter 13 of the WSDOT Bridge Design Manual (WSDOT 2006), shown in Figure The HS20 Truck load consists of three point loads that are representative of a three-axle truck. The leading point load is an eight kip point load corresponding to the front axle of the truck. The center axle of the truck is represented by a 32 kip point load spaced 14 ft from the leading point load. Trailing this load is another 32 kip load that has variable spacing between 14 ft and 30 ft from the central axle load. The location of the trailing axle is positioned so that it causes the maximum effect in a given member. Furthermore, the HS20 Truck load is moved along the bridge until the maximum load for a particular member is determined. 51

74 lbs The HS20 Lane load has two main components: a distributed load of 640 ft and two different point loads, applied one at a time, which are known as moment and shear riders. The moment rider is an 18 kip load and the shear rider is a 26 kip load. In a truss bridge the moments are carried by the chord members and the shear is carried by the web members. Thus, for chord members the HS20 lane load is calculated by using the distributed load in combination with the 18 kip point load and for web members the HS20 Lane load is a combination of the distributed load and the 26 kip point load. The distributed load and the appropriate point load are positioned along the bridge to cause the maximum axial force for the member under consideration. Figure 3.12: Schematic of the HS20 Truck load and the HS20 Lane load Axial load influence lines were used to determine the position of the HS20 Truck load or the HS20 Lane load that cause the maximum loads for the members framing into a particular joint. These influence lines were extracted directly from the SAP2000 analysis and used to determine both maximum envelope loads as well as point-in-time, or concurrent, loads for the joint in question. For example, Figure 3.13 shows the influence lines for each member framing into Joint L3 from BR 31-52

75 Member Influence 36. Along the horizontal axis is the distance along the bridge along which the truck will travel; starting at Joint U0 and heading towards Joint U13. The vertical axis is the axial load influence that each member experiences as the load is moved from one end of the bridge to the other L3-L2 L3-U2 L3-U3 L3-U Distance Along Roadway (ft) Figure 3.13: Axial load influence lines for Joint L3 of BR To find the maximum force that Member L3-L2 experiences under the HS20 Truck loading, the trailing axle load of 32 kips is placed at the peak of the influence line corresponding to Member L3- L2. The central axle load of 32 kips and the leading axle load of 8 kips is placed to the right-hand side of the curve at an equal spacing of 14 feet. The influence values extracted at the axle locations are multiplied by the axle load that they correspond to and are summed to determine the maximum envelope load for the member. Figure 3.14 shows where along the bridge the HS20 Truck was 53

76 placed for Member L3-L2 as well as the values of influence that correspond to the axle load locations. Using these values, the maximum envelope load for Member L3-L2 is kips kips kips kips 32 in tension. This procedure was repeated for each member in the joint to determine the maximum envelope loads for the joint. Figure 3.14: Maximum envelope load influence values for HS20 Truck loading of Member L3-L2 on BR While maximum envelope loads are sufficient to check element capacities and employ some gusset plate checks, it is was necessary to determine the concurrent loads for use in the detailed analyses and for checking the gusset plate shear strength per the FHWA Guide. Concurrent loads are found by finding the values of influence for each member in the connection that corresponds to a fixed location of the axle load. When the truck is at a position that gives the maximum envelope load for 54

77 Member L3-L2, there are four additional sets of influence values for the remaining members. These values of influence are used to determine the axial load in those members for the fixed truck location. This set of concurrent loads is denoted as a load case herein. For any joint on the bridge in question, the number of members framing into that joint corresponds to the number of load cases for that joint. For example, Joint L3 from BR has five members framing into it and so there are five concurrent load cases for that joint. The five HS20 Truck load cases for Joint L3 on BR are shown in Table 3.1. The cells that are highlighted represent the maximum envelope load for each particular member of the gusset plate. Note that in this instance, Load Cases 2 and 5 and 3 and 4 have the same element loads and resulting from the same truck placement along the bridge. Table 3.1: HS20 Truck load cases for Joint L3 on BR HS20 Truck Loads (k) Case # L3-L2 L3-U2 L3-U3 L3-U4 L3-L As was mentioned previously, the HS20 Lane load consists of a distributed load and a point load. Using the same influence lines from before, maximum envelope loads, as well as concurrent loads, can be found for this loading scenario, as illustrated in Figure 3.15 for Member L3-L2. To determine the maximum envelope load for a member, the point load is placed along the influence line where it produces the highest magnitude load. For example, Member L3-L2 is a chord member and so an 18 kip point load is placed at the peak influence value of 1.41 resulting in a total load of kips kips Added to this is the effect of the distributed load. Because this particular 55

78 member is controlled by tension, the axial load due to the distributed lane load is found by finding the area under the positive portion of the influence line and multiplying it by the distributed load. Figure 3.15: Position of the HS20 point load and lane load for Member L3-L2 of BR Concurrent loads for a joint may then be found with each load case again corresponding to a particular members force being at its maximum value. This is done by simply placing the point load and distributed loads at the same locations used for the member whose force is a maximum on the other members influence lines. For example Table 3.2 shows the five load cases for the HS20 Lane load for gusset plate L3 from BR The highlighted cells correspond to the maximum envelope load for each member in the connection. The loads from the HS20 Lane load and the HS20 Truck load are then compared and the cases which give the largest loading govern and were used for future analyses. 56

79 Table 3.2: HS20 Lane load cases for Joint L3 on BR HS20 Lane Load (k) Case # L3-L2 L3-U2 L3-U3 L3-U4 L3-L Model Verification After the models were completed and the loads were determined, it was necessary to ensure that the results were accurate. This was done by comparing the loads from the stress sheets from the original design drawings to those produced from analysis. Because the live loads used in the original bridge design were not the same as the HS20 live loads, model verification was done by comparing only the dead loads. The comparisons for all three bridges are shown Table 3.3 through Table 3.5. Loads are only reported for half of the bridge members as the bridges are symmetric about the midspan. The results shown illustrate that the dead loads from the models match rather well with the loads taken off the stress sheets. The only major discrepancies that occur typically happen with lightly loaded hanger members. 57

80 Table 3.3: Comparison of dead loads for BR N Bridge Member ID Dead Load (k) Stress Sheet Model % Difference L0-L % L0-U % L1-L % L1-U % L2-L % L2-U % N L2-U % L3-L % L3-U % L4-U % U1-L % U1-U % U2-U % U3-L % 58

81 Table 3.4: Comparison of dead loads for BR Bridge Dead Load (k) Member ID Stress Sheet Model % Difference L1-U % L1-U % L1-U % L1-L % L2-U % L2-L % L3-U % L3-U % L3-U % L3-L % L4-U % L4-L % L5-U % L5-U % L5-U % L5-L % L6-U % L6-L % L7-U % L7-U % L7-U % L7-L % L8-U % L8-L % L9-U % L9-U % L9-U % L9-L % L10-U % L10-U % L10-L % L11-U % L11-L % L12-U % L12-U % L12-U % L12-L % L13-U % U1-U % U1-U % U2-U % U3-U % U4-U % U5-U % U6-U % U7-U % U8-U % U9-U % U10-U % U11-U % U12-U % 59

82 Table 3.5: Comparison of dead loads for BR Bridge Member ID Dead Load (k) Stress Sheet Model % Difference L1-L % L1-U % L1-U % L1-L % L2-U % L2-U % L2-L % L3-U % L3-U % L3-L % L4-U % L4-L % L5-U % L5-U % L5-L % L6-U % L6-U % L6-L % L7-U % L7-U % L7-L % L8-U % L8-U % L8-U % L8-L % L9-U % L9-U % L9-L % L10-U % L10-L % L11-U % L11-U % U0-U % U1-U % U2-U % U3-U % U4-U % U5-U % U6-U % U7-U % U8-U % U9-U % U10-U % 60

83 Chapter 4: Gusset Plate Modeling and Observed Behavior used to Develop the TEP 4.1 General In order to develop the TEP, several detailed finite element models were created of selected joint subassemblies from the three previously described Washington State bridges and Joint U10 from the I-35W Mississippi River Bridge. The joints were selected because they were found to be highly stressed based on initial Whitmore stress calculations and/or they represented a variety of geometries likely to be encountered in the field. Once the joints were selected, a parametric study was conducted with the purpose of characterizing truss bridge joint behavior using the local finite element models. Variations in the gusset plate thicknesses, load distributions and connection geometries were used to develop a basic understanding of the stress distribution of the gusset plate. The parametric study was also used to help identify the important factors involved in elastic and inelastic gusset plate buckling. The results of the parametric study were then used to develop the TEP. This chapter describes the modeling methods used, the different connections that were modeled, the observed gusset plate behavior and development of the TEP. A more detailed discussion on these topics can be found in Wang (2011). 4.2 Local Finite Element Model Definitions For investigating the behavior of the truss bridge joints, 3D models were created using the ANSYS v11.0 finite element analysis package. Figure 4.1 gives an example of a typical gusset plate model with the boundary and loading conditions shown. The gusset plates and the members near the connection were modeled using a dense mesh of shell elements. The members were then 61

84 transitioned to beam elements at a distance of 2d away from the gusset plate edge, where d is the depth of the member being considered. These beam elements were extended to the next panel points of the truss where all degrees of freedom, except translation in the axial direction of the member, were restrained. At these panel point locations, the axial loads calculated from the global analysis were applied (Wang 2011). Figure 4.1: Example of 3D finite element model of a truss bridge gusset plate with boundary and loading conditions shown Non-linear material properties were used and non-linear geometry was considered in the analysis to help model gusset plate buckling and the behavior under high stress. Rivets and rivet holes were not explicitly modeled in the analysis as the relative increase in accuracy did not offset the required computational time. Members were connected to the gusset plates at the center of each rivet location by constraining the node of the plate to the adjacent node of member. This type of rivet representation assumes that the rivets remain completely rigid. Contact between the plates and the members was not modeled. An appropriate mesh refinement study was performed to establish a 62

85 mesh density that could accurately exhibit the stress distributions of the gusset plate, while maintaining computing efficiency (Wang 2011). To provide confidence in the modeling procedure several analyses were performed that could be compared to previous experimental results or other analytical investigations. First, a model of Joint U10 from the collapsed I-35W Mississippi River Bridge was developed. Results from this analysis were compared to the results from the analyses performed by Ocel and Wright (2008). Similarly, the specimen described in Whitmore (1952) was also modeled so that the analytical results could be compared to experimental results. These comparisons showed that the selected modeling methods could adequately reproduce the observed stress distributions from these studies. A more detailed description of the development and validation of these finite element analyses can be found in Wang (2011). 4.3 Joint L2 from BR N Joint L2 from BR N was selected because it represents a very common configuration and was one of the more highly stressed plates based on initial Whitmore stress calculations. Joint L2 is a five member connection along the lower chord of a Warren-type drive through truss bridge. Figure 4.2 shows a photograph as well as a schematic showing the types of members framing into the connection. As is typical with this type of truss, the bottom chords, Member L2-L1 and Member L2- L3 are in tension. The diagonal, Member L2-U1, is in tension while the other diagonal, Member L2- U3, is in compression. The vertical hanger, Member L2-U2, is also in tension in this connection; however, the magnitude of the load it carries is considerably smaller than that of the other members. In addition to the five members framing into the gusset plate, there is a large floor beam that is fastened to the interior main gusset plate. As shown in Figure 4.2, all of the members framing into this connection are comprised of built up members. The box-type members are built using 63

86 channel members and plates fastened together with rivets. The I-shape members are composed of four angles riveted to a single plate that is the web of the shape. Figure 4.2: Photograph and schematic of Joint L2 from BR N A unique aspect of Joint L2 is that the chord members are spliced together at a location that is offset from the work point of the joint. Because the chord member L2-L3 is more heavily loaded, the splice has been offset so that this member utilizes more of the main gusset plates to transfer its load. At the splice location there is also a small splice plate riveted along the top of the two chord members as shown in Figure 4.2. In addition to the top splice plate, the bottom of the chord members are spliced by a single gusset plate that is used to connect the wind bracing along the underside of the bridge deck. Both the main gusset plate and the top splice plate are 1/2 in. thick, while the wind bracing gusset plate is 3/8 in. thick. The gusset plates, as well as the splice plates, are designated on the structural drawings as ASTM A94-46 (ASTM 1946) silicon steel with a specified yield strength of 45 ksi. The members are built using A7-39 steel with a specified yield strength of 33 ksi. When developing the local model, shown in Figure 4.3, it was necessary to make additional a few assumptions about the loading conditions and restraints. The previously described floor beam is connected to the inner main gusset plate by a web angle connection. Loads from this floor beam 64

87 were applied at the centerline of the rivets where the angle is connected to the beam web. In addition to the loads, out-of-plane displacement of the gusset plate was restrained where the angle is connected to the plate. As shown in Figure 4.3 the wind gusset was also included in the model; however, the wind bracing members were not included. An additional out-of-plane displacement restraint was also added at the wind gusset location (Wang 2011). Figure 4.3: Rendering of the finite element model for Joint L2 from BR N 4.4 Joints L9 and L1 from BR Two gusset plate connections were chosen from BR due to their relatively large Whitmore stresses and their unique geometrical configurations, namely Joints L9 and L1. Plate and member material properties were ASTM A7-39 (ASTM 1939) with specified minimum yield strength of 33 ksi. Joint L9, shown in Figure 4.4, is a five member connection along the lower chord of a cantilevered truss bridge where one of the chord members is a zero-force member. This member, L9-L10, has a sliding pin connection (mentioned in the previous chapter) on the Joint L10 end and a pin connection to Joint L9. The loaded chord, Member L9-L8, the diagonal, Member L9-U10, and the vertical, Member L9-U9, are all in compression while the diagonal, Member L9-U8, is in tension. The 65

88 axial loads in the vertical member are significantly smaller than those in the other members. Members L9-U10 and L8-L9 are built up box shaped members consisting of two channels connected with overlapping plates. Member U8-L9 is a built up I-shaped section that is constructed using four angles and one plate and Member U9-L9 is a rolled I-shape. Figure 4.4: Photograph and schematic of Joint L9 from BR Joint L9 has two exterior splice plates to connect the loaded chord to the main gusset plate. The main gusset plate and the splice plates are all 1/2 in. thick. As shown in Figure 4.4, there is a large pin that is part of the expansion joint system for the drop-in simple span portion of the bridge; however, this pin was not modeled because there is no load transferred to it. For this particular joint there is a smaller plate connection for the wind bracing members that provides out-of-plane displacement restraints along the lower edge of the interior main gusset plate. Additionally, there is a single angle connection on the inner portion of the main gusset plate where the sway bracing is connected which provides similar restraints. All of the aforementioned restraint conditions were implemented in the finite element model which is shown in Figure 4.5 (Wang 2011). 66

89 Figure 4.5: Rendering of the finite element model for Joint L9 Joint L1 is a lower chord connection along the back span portion of the cantilevered truss bridge and is shown in Figure 4.6. It connects five members; however, the chord, Member L1-L0, is a zero force member. Joint L1 was selected for detailed analysis after a significant portion of this study had already been completed. It was selected because it had been identified as being overstressed based on the evaluation procedure which was developed and will be discussed later in this report. The loaded chord, Member L1-L2, as well one diagonal, Member L1-U0, is loaded in tension, while the vertical hanger, Member L1-U1, is loaded in compression. The other diagonal, Member L1-U2, can be loaded in either tension or compression depending on the location of the live load along the bridge. The chord members are built up box shaped member using two channels and two plates while the diagonal members and hanger are rolled I-shapes. 67

90 Figure 4.6: Photograph and schematic of Joint L1 from BR At this joint, the chords are spliced at the work point using a single 3/8 in. thick splice plate located along the top of the chord members. The main gusset plate is also 3/8 in. thick. A 5/16 in. thick wind bracing gusset plate along the bottom side of the chords acts as a splice and provides out-of-plane displacement restraint for the main gusset plate. Similar restraint is provided by small angle connections that are used to connect the sway bracing to the joint. These restraints were incorporated into the finite element model shown in Figure 4.7 (Wang 2011). Figure 4.7: Rendering of the finite element model for Joint L1 from BR

91 4.5 Joints L5 and U3 of BR Two joints, L5 and U3, were chosen from this bridge based on initial estimations of their stress states and for their unique configurations. The steel used for the members and the plates all conform to ASTM A7-24 (ASTM 1924) with a specified minimum yield strength of 30 ksi. Most connections on BR are quite different in their configurations than those mentioned previously. Joint L5 is a four member joint along the lower chord of a cantilevered truss bridge and is shown in Figure 4.8. The chords, Members L5-L4 and L5-L6, as well as the diagonal, Member L5-U4, are in compression while the vertical hanger, Member L5-U5, is in tension. The joints on BR are different than other joints studied as the gusset plates run along the inside of the two parallel C- shaped chord members. Additionally, the vertical hanger member continues to the bottom edge of the main gusset plate. The chord members are spliced at the work point of the joint, however, because both members are in compression the loads are transferred by direct bearing. The chords are also spliced using multiple splice plates that are layered one on top of the other. The outer splice plate and inner splice plates are 3/8 in. thick and 3/4 in. thick, respectively. The main gusset plate is 3/8 in. thick. The chord members are constructed using two angles and a single plate to form a C- shaped member. The diagonal and vertical members are standard rolled I-shapes. 69

92 Figure 4.8: Photograph and schematic of Joint L5 from BR There are two plates that are used to connect the wind bracing to the joint. The bottom wind plate runs across the chord members acting as a splice and providing restraint against out-of-plane movement of the joint. The top wind plate is attached to the top of the inside chord member and so it acts as a splice for half of the chord while providing additional out-of-plane displacement restraint. Similarly, a small angle is used to connect sway bracing to the inner gusset plate which provides similar displacement restraints. All of the previously mentioned restraint conditions were implemented into the finite element model shown in Figure 4.9 (Wang 2011). Figure 4.9: Rendering of the finite element model for Joint L5 from BR

93 Joint U3 from BR was also selected for detailed modeling and is shown in Figure This joint is an upper chord connection along the back span portion of a cantilever truss bridge and has four members framing into it. Both of the chords, Members U3-U2 and U3-U4, as well as the diagonal, Member U3-L2, are in tension, while the vertical hanger, Member U3-L3, is in compression. Similar to Joint L5, the 3/8 in. thick main gusset plates are on the inside of two parallel C-shaped chords. The chords are spliced at this joint; however, the splice location is offset a considerable distance from the work point of the connection. The chords are spliced using two 5/16 in. thick splice plates and the main 3/8 in. thick gusset plates, with the splice plates located on the outside of the chords. Similar to Joint L5, the vertical compression member extends all the way to the top edge of the gusset plate. Along the top of the chord members, several plates are used to connect wind and sway bracing members, which also provide out-of-plane displacement restraint to the joint itself. The chord members are built up using two angles and a single plate to form a channel shape, while the diagonal and the vertical members are rolled I-shapes. Figure 4.11 shows the finite element model for this gusset plate connection (Wang 2011). Figure 4.10: Photograph and schematic of Joint U3 from BR

94 Figure 4.11: Rendering of the finite element model for Joint U3 from BR Joint U10 of I-35W Mississippi River Bridge Joint U10 was modeled the I-35W Mississippi River Bridge for several reasons. First, this joint represents a key data point in that many studies have indicated it was highly stressed at the time of collapse. Second, the results of the local modeling done here can be compared with the results from Ocel and Wright (2008) who modeled this joint in the context of the entire bridge. Both the plate and member materials conformed to ASTM A441 with a specified minimum yield stress of 50 ksi. Joint U10 is a five member joint along the top chord of a cantilever truss bridge and is shown in Figure The location of the joint is at the inflection point of the truss which means that one chord, Member U10-U9, is in tension while the other chord, Member U10-U11, is in compression. The diagonal, Member U10-L11, and the vertical hanger, Member U1-L10, are in tension while the remaining diagonal, Member U10-L9, is in compression. The chord members are spliced at the work point of the connection with 1/2 in. thick internal splice plates front and back and 3/8 in. thick 72

95 internal splice plates top and bottom. Along the top of the chords is a 3/8 in. thick wind gusset plate that connects the wind and sway bracing. The main gusset plates are 1/2 in. thick and overlap the members. The chord members, as well as Member U10-L9, are comprised of four plates welded together to form a box shaped member. The remaining members are rolled I-shapes. Figure 4.12: Photograph and schematic of Joint U10 from I-35W At this particular joint wind bracing frames into the side of the inner main gusset plate. This bracing is connected to the gusset plate by utilizing smaller plates similar in configuration to the wind gusset plate. These connections provided out-of-plane displacement restraint for the connection. These conditions were modeled in the finite element analysis of the joint shown in Figure 4.13 (Wang 2011). 73

96 Figure 4.13: Rendering of the finite element model for Joint U10 for I-35W 4.7 Gusset Plate Parameters Considered The effect of truss bridge joint geometry on the behavior of the joint s gusset plates was studied by selecting a wide variety of joints with considerably different layouts. Using actual joints to explore the effects of gusset plate configuration was seen as advantageous over creating modifications of a base joint geometry because it allowed for the analysis of connections that would be encountered in practice. If a generic gusset plate connection had been chosen and then its geometry artificially varied in the study, it may not have been possible to capture the behavior of some of the more unusual joint geometries. The thicknesses of the main gusset plates for each joint studied were varied in order to establish the effect of gusset plate slenderness on elastic and inelastic buckling. Gusset plate thicknesses of 1/8 in., 1/4 in., 3/8 in., and 1/2 in. were used for all of the joints analyzed, except for Joint L5 of BR for which the 1/2 in. thickness was not examined. 74

97 The effect of load distribution on the joints was studied by varying the relative axial loads in the connected elements. For the joints belonging to the bridges selected from the WSDOT inventory (BR N, BR and BR ) truss member axial loads were varied by utilizing the load cases described in Chapter Chapter 3:. In the case of Joint U10 from I-35W, the loads for this joint were based upon the loads estimated at the time of collapse by Ocel and Wright (2008). In order to study the effect of load distribution on this joint, five load distributions had to be created. These five distributions were created by taking the load in one member and increasing it by roughly 15% and then rebalancing the forces in the other members to achieve equilibrium. Table 4.1 shows the reported member loads at the time of collapse as well as the loads for the five distributions (Wang 2011). Table 4.1: Estimated member loads at collapse for Joint U10 of I-35W and the five load distributions used in parametric study Estimated Member Loads at Collapse (k) U10-U9 U10-L9 U10-L10 U10-L11 U10-L Load Distributions (k) Case # U10-U9 U10-L9 U10-L10 U10-L11 U10-L Gusset Plate Yielding This section discusses the observed onset and progression of gusset plate yielding in the selected joints and the proposed TEP for evaluating the yield capacity of a gusset plates in truss bridge joints. 75

98 4.8.1 Yielding Observations Each joint model was analyzed for the load distributions discussed previously by linearly increasing the load well into the inelastic range. This allowed for the onset of yielding to be identified and the progression of yielding to be observed. The loads under which these gusset plates began to yield was often two or three times greater in magnitude than the design loads calculated in Chapter Chapter 3:. For the purposes of illustration, the yielding behavior of Joint U10 of I-35W will be discussed herein, although similar behaviors were found with the other gusset plate connections studied (Wang 2011). Figure 4.14 shows an example of the progression of yielding as the loads are linearly increased. The contours shown in this Figure are Von Mises stress contours where areas that are black in color are regions where the specified yield stress of the material has been exceeded. Also included in this Figure is a plot showing how the percentage of area in the gusset plate that has yielded increases with load in the compression diagonal (Wang 2011). 76

99 Figure 4.14: Progression of gusset plate with increase in truss member loads. Stress contours show Von Mises stress in ksi. (a) 0% Yielded area, (b) 0.3% Yielded area, (c) 6.5% Yielded area, (d) 10.5% Yielded area and (e) Force in the compression diagonal vs. yielded gusset plate area Examining the results in Figure 4.14 it was observed that once yielding of the gusset plate has initiated, the rate of increase of in the total yielded area of the gusset plate increases quite rapidly with only a marginal increase in the member load. Using these observations it was determined that the initiation of yielding would be defined henceforth as when 0.5% of the total gusset plate area has achieved a Von Mises stress equal to or greater than the specified yield stress of the gusset plate material. While this is by not by means a state of gusset plate failure, the initiation of yielding would assuredly be a concern for the owners of the bridge. In order to determine the member loads at the onset of significant yielding, image files from ANSYS were exported to an image processing algorithm developed in MATLAB. This algorithm counts the number of pixels that comprises the 77

100 yielded area of the plate and compares it to the total number of pixels for the entire plate. Oftentimes, the load steps did not coincide with exactly 0.5% yielded area, so it became necessary to linearly interpolate between load steps to extract the loads at initial yielding. Figure 4.15 depicts what the initiation of yielding looks like on some of the gusset plates studied, where the gray area is the area that has achieved stress higher than the specified yield stress of the material (Wang 2011). Figure 4.15: Onset of significant yielding for the gusset plates (a) Joint L2 BR N, (b) Joint L9 of BR 31-36, (c) Joint L5 of BR , and (d) Joint U10 of I-35W When the Whitmore stress is calculated for the compression member U10-L9 from I-35W at the onset of yielding, it was found to be 29.4 ksi, or 59% of the specified yield stress of the gusset plate steel. This demonstrates that even though the gusset plate has begun to yield, the conventional check for yielding is not adequately capturing this behavior. One explanation for this is that the area where yielding originates in the plate is a location where the stresses from the chord members and the diagonal members interact to produce a combined stress states that is larger than the uniaxial Whitmore stress. Furthermore, the intent of the Whitmore stress calculation is to estimate the maximum uniaxial stress at the end of a truss member. However, in the analysis performed yielding 78

101 was not generally observed at the end of a member but rather away from the ends and was dictated by Von Mises stresses. Figure 4.16 shows a depiction of how uniaxial stresses from the ends of the diagonals and the shear stresses caused by the chord members causes an interference of stresses in a small, triangular area of the gusset plate that is bounded by the rivet lines from the chord and the hanger and the end of the diagonal members. When other gusset plate connections were examined, it was found that yielding of the gusset plate always initiated in those critical areas. Figure 4.16: Depiction of the interference of stresses in the critical area of a typical gusset plate Proposed Yielding Check for the TEP In order to conservatively predict the onset of gusset plate yielding, a number of simplifying assumptions were made about gusset plate geometry and member loads. Consider a simple five member gusset plate like that shown in Figure

102 Figure 4.17: Simplified gusset plate geometry used for development of TEP This gusset plate has two diagonal members at angles 1 and 2 measured from the horizontal. The vertical hanger is neglected here as typically it is lightly loaded in these types of joints. Whitmore stresses for these diagonal members can be calculated and are denoted as w1 and w2 as shown in Figure As discussed previously, yielding of the gusset plate was observed to begin away from the ends of the members and was attributed to the interaction of stresses in the so-called critical area. In order to predict the stress that occurs in these areas several assumptions about the combination of stresses, gusset plate geometry and member loads were made. First it was assumed that the Whitmore stresses for the diagonal members are uniaxial stresses and therefore, the shear stress,, at these locations is zero. Next, it is assumed that these Whitmore stresses are principle stresses, that is w and w Subsequently, in order to replicate the interference of stresses observed these principle stresses may be combined to form a single stress state. Using this combination of stresses and assuming a Von Mises Yield criterion for plane stress gives the result shown below: 80

103 (5.3.1) y where 1 and 2 are principle stresses and y is the yield stress of the gusset plate. Given the Von Mises yield criteria it is possible to make additional assumptions that would ensure the worst stress state. First, it was assumed that both of the diagonal members were at a 45 angle with respect to the horizontal thus making them orthogonal to each other (i.e. 45 ). The assumption that 1 2 the members are orthogonal to one another is conservative because these stress states can be combined directly without having to rotate them using Mohr s circle. If the stress states were not orthogonal, the subsequent Mohr s circle transformation would decrease the magnitude of the principle stresses and thus decrease the Von Mises stress. The next conservative assumption that was made was that each member had loads of equal magnitude but opposite sign. When these members have equal but opposite loads their respective principle stresses, 1 and 2, are equal and opposite thus indicating that yielding of the plate would occur when / 3. This condition 1 y provides the largest Von Mises stress state and so is most conservative. Combining all of the previously described assumptions, the onset of yielding of a gusset plate on a bridge could be predicted by determining the maximum Whitmore stress, joint and checking it against the yield check shown below: w, maz, for all members framing into the Fy w,max (5.3.2) 3 where F is the yield stress of the gusset plate. y 81

104 4.8.3 Comparison of the TEP Yielding Check with Analytical Results In order to confirm the assumptions made under the yielding check of the TEP, the loads at the onset of initial yield were extracted from the ANSYS models. Using the loads, a demand-to-capacity ratio was calculated for each member of the joint in question where the capacity was taken as the effective area as defined by the Whitmore section multiplied by F / 3. A demand-to-capacity ratio greater than 1.0 means that the TEP yield check is indicating that the gusset plate has begun to yield. In addition to the TEP yield capacity, the capacity for each limit described in the FHWA procedure was calculated. The largest demand-to-capacity ratio, considering all described limit states, is then taken as the FHWA demand-to-capacity ratio for the entire connection. Table 4.2 through Table 4.5 show the demand-to-capacity ratios at the onset of yielding for each member using the yielding check of the TEP as well as the controlling ratio for the entire joint using the FHWA evaluation procedure (Wang 2011). This Figure clearly shows that the TEP yielding check is able to capture the onset of initial yielding, while the FHWA procedures would suggest that the gusset plate is adequate at this load particular level. y Table 4.2: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint L2 of BR N Connection ID Triage D/C L2-L Load Case # Case 1 Case 2 Case 3 Case 4 Case 5 FHWA D/C Triage D/C 1.21 FHWA D/C Triage D/C FHWA D/C Triage D/C FHWA D/C Triage D/C L2-U L2-U L2-U L2-L FHWA D/C

105 Table 4.3: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint U10 of I-35W Connection ID Triage D/C U10-U Load Case # Case 1 Case 2 Case 3 Case 4 Case 5 FHWA D/C Triage D/C 0.60 FHWA D/C Triage D/C FHWA D/C Triage D/C FHWA D/C Triage D/C U10-L U10-L U10-L U10-U FHWA D/C 0.98 Table 4.4: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint L9 of BR Connection ID Triage D/C L9-L Load Case # Case 1 Case 2 Case 3 Case 4 FHWA D/C Triage D/C 1.01 FHWA D/C Triage D/C 0.97 FHWA D/C Triage D/C 1.01 L9-U L9-U L9-U FHWA D/C

106 Table 4.5: Demand to capacity ratios using the TEP and the controlling FHWA capacity for Joint L5 of BR Connection ID Triage D/C L5-L Load Case # Case 1 Case 2 FHWA D/C Triage D/C 1.24 L5-U L5-U L5-L FHWA D/C 0.71 It should be noted that the FHWA horizontal shear capacity check for Joint L5 of BR was excluded from the demand to capacity ratio because there is no shear line that can be drawn across the plate that does not bisect the member. This makes shear failure along this horizontal plane unlikely. Figure 4.18 shows a schematic of this particular connection and how the horizontal shear plane must include the vertical member. Additionally, for this particular joint there were only two distinct load cases due to the fact that two of the four possible four load cases were identical. Figure 4.18: Schematic of Joint L5 of BR showing horizontal shear plane passing through hanger member 84

107 4.9 Comparison of Block Shear with the TEP Yield Check To ensure that the TEP yield check is conservative with respect to the block shear limit state, a parametric study was performed using two generalized member-to-gusset plate connections. The first connection type is a symmetric connection that would be typical for a hanger or diagonal member while the second connection type is non-symmetric as is typical for a chord connection. The variables defining the connection geometries, as shown in Figure 4.19, are: L vg = gross shear length, L vn = net shear length, L tg = gross tension length, L tn = net tension length, n rt = number of rivets along the tension line, n rv = number of rivets along the shear line, d = rivets diameter, and t p = gusset plate thickness. Assuming that the rivets are equally spaced at a center-to-center distance that is a multiple of their diameter, d, the connection geometry parameters may be written as: L d n 1 (5.4.1) vg rv 1 n 1 L d (5.4.2) vn rv L d n 1 (5.4.3) tg rt 1 n 1 L d (5.4.4) tn rt 85

108 Figure 4.19: Basic connection geometry and definitions The block shear resistance of a connection is given in the FHWA Guide as: If A 0. 58A tn, Then P 0. 58F A F A vn r Otherwise P 0. 58F A F A r bs (5.4.5) bs u vn y vg y tg u (5.4.6) tn where is taken as 0.8. For the failure surface shown in Figure 4.20(a) and considering Equations (5.4.1) through (5.4.4), the block shear strength of the connection may be re-written as: Pr t d p n 1 F 1 n 1 bs 0.58Fy rv u rt (5.4.7) Pr t d p bs 1 n 1 F n F u rv y rt (5.4.8) 86

109 This derivation of the block shear resistance conservatively neglects a small section of the plate, as shown in Figure 4.20(a). Similarly, considering the Whitmore section shown in Figure 4.20(b), the TEP yield force may be written as: Pr t d p n n 1 1 tan30 rt rv Fy (5.4.9) 3 Figure 4.20: (a) Block shear failure surface for a chord connection and (b) Whitmore section for a chord connection used for TEP stress calculation Equations (5.4.7) through (5.4.9) are then used to compare the block shear resistance to the resistance calculated using the TEP yield check. Figure 4.21 shows the ratio of block shear resistance to the TEP yield resistance for a reasonable range of connection parameters and material strengths. It should be noted that the ASTM specification through 1949 specified that the yield stress for structural steel, F, be ½ the tensile stress, F, while meeting an additional specified lower bound y u (Brockenbrough 2002). Therefore, the range of F / F considered in Figure 4.21 is sufficient. Additionally, it has been observed in the numerous truss bridge joint drawings examined that the center-to-center spacing of the rivets is not likely to be less than 3d. Therefore, using values of α equal to 3 and 4 would be representative of the majority of connections. Using these parameters, y u 87

110 Figure 4.21 shows that the block shear capacity of a connection is never less than the TEP yield capacity. The same process was performed for the block shear failure surface and Whitmore section of a typical diagonal or hanger connection, as shown in Figure Equations (5.4.10) through (5.4.11) and Equation (5.4.12) are the respective block shear and TEP yield capacity for this connection configuration. The ratio of block shear capacity to TEP yield capacity for this connection type using the same parameters considered previously is shown in Figure As shown, the block shear strength is always greater than the TEP yield capacity. Thus, these results demonstrated that the TEP yield capacity is conservative relative to block shear for the range of connection parameters expected in truss bridge joints. Pr t d p n 1 F 1 n 1 bs 1.16Fy rv u rt (5.4.10) Pr t d p 1 n 1 F n F bs u rv y rt (5.4.11) Pr t d p n 2n 1 rt 1 tan30 rv Fy 3 (5.4.12) 88

111 Figure 4.21: Ratio of block shear capacity to TEP Yield capacity for chord connections with various connection parameters Figure 4.22: Block shear failure surface for a diagonal or hanger connection and (b) Whitmore section for a diagonal or hanger connection used for TEP stress calculation 89

112 Figure 4.23: Ratio of block shear capacity to TEP yield capacity for diagonal or hanger connections with various connection parameters 4.10 Gusset Plate Buckling This section discusses the observed buckling behavior of gusset plates and the proposed method for evaluating the buckling capacity of a gusset plate connection as a part of the TEP Buckling Observations In order to study gusset plate buckling capacity, a parametric study was performed whereby the thickness of the main gusset plates of the selected joints was varied. By varying this parameter, the effect of the gusset plate slenderness, L/t, on elastic and inelastic buckling could be investigated. Using the ANSYS models described previously, the load distributions described in Chapter 4 were linearly increased until the gusset plate(s) buckled or until convergence failure of the analysis occurred. In the majority of cases the observed buckling behavior was inelastic, except for the cases where very thin plates, typically 1/8 in. thick, were used where elastic buckling was observed. Gusset plate buckling was not observed in any of the joints from BR because the compression members extended all the way to the edge of the chord members, making it 90

113 impossible for the main gusset plate to buckle. When gusset plate buckling was observed, the buckled shape of the main gusset plate always occurred in a symmetric, or sidesway mode shape. Figure 4.24 shows this particular behavior for Joint L2 of BR N and Joint U10 of I-35W. The deformations in this Figure have been amplified by a factor of approximately 40 in order to better depict the buckling behavior (Wang 2011). (a) (b) Figure 4.24: Buckled shapes of (a) Joint L2 of BR N and (b) Joint U10 of I-35W Where gusset plate buckling was observed, nodal displacements of the gusset plate were recorded at two locations. The first location was along the centerline of the compression member starting at the end of the member and extending to the next intersecting line of rivets from an adjacent member. The second location was along the free edge of the gusset plate, typically from the last row of rivets along the compression diagonal to the first row of rivets belonging to the chord member. These two locations for a typical joint can be seen in Figure

114 Figure 4.25: Locations where nodal displacements were recorded for gusset plate buckling As the load in the compression diagonal was increased, out-of-plane deformations at the aforementioned locations were recorded in order to produce load-deformation plots, like those seen in Figure This Figure shows how the gusset plate deforms out-of-plane as the load in the compression member is increased which eventually gives way to buckling of the plate itself. 92

115 Distance Along Compression Line (in) Out-of-Plane Displacement (in) Figure 4.26: Typical progression of out-of-plane displacement of the gusset plate along the compression diagonal It was necessary to determine whether buckling occurred first along the free edge line of the plate or along the line parallel with the compression diagonal. To do this, a single node was selected at the approximate center of each of those buckling lines. Then, compressive force versus out-of-plane displacement was plotted at those nodal locations. Next, the buckling load was determined by finding the location where the initial tangent was intersected by a tangent line representing 15% of the initial tangent slope. This point of intersection was taken as the buckling load, P, as shown in Figure 4.27 (Wang 2011). cr 93

116 Figure 4.27: Determination of the buckling load using compressive force versus out-of-plane displacement When the buckling load was calculated using the out-of-plane displacements at the previously described gusset plate locations, it was found that they were typically within 5% of each other which implies that buckling at these points was occurring essentially simultaneously. Thus, for the remainder of the study the buckling load of the gusset plates was determined using the maximum out-of-plane deformation parallel to the compression diagonal. It should be noted here that because contact between the gusset plates and the truss members was not modeled and some of the gusset nodes would move slightly into the members along the diagonal and the plate edge. While this behavior is not possible in reality, it is conservative for estimating the gusset plate buckling capacity because the unbraced lengths of the plate used in the finite element analysis are slightly longer than they would be in the field (Wang 2011). 94

117 Proposed Buckling Check for the TEP After establishing a method for determining the critical buckling load from the finite element analysis data, a method for checking the buckling capacity of gusset plates was developed. Using AASHTO Articles and as a basis, three different methods for determining unbraced length, L, and the critical buckling stress, F, were explored. The first method, denoted as the cr Thornton method, was proposed by Thornton (1984) and was described previously in Chapter 2. The second method, denoted as the Modified Thornton method, was proposed by Yam (1994) and was also reviewed in Chapter Chapter 2:. This method utilizes a 45 Whitmore projection angle to establish F and the unbraced length, L, is taken as the centroidal distance from the end of the cr compression member to the nearest intersecting line of rivets. The third method, denoted as the Yoo method, was proposed by Yoo et al. (2008) and is similar to the Thornton method except it uses 45 rather than 30 for the dispersion angle. The geometries used in those three methods for determining the critical buckling parameters are shown in Figure Figure 4.28: (a) Thornton Method for unbraced length, (b) Modified Thornton Method for unbraced length, and (c) Yoo Method for unbraced length. For each joint, the critical buckling stress was calculated using these three methods and was compared with that found from the finite element analysis as described previously. This was done by plotting buckling curves obtained with the three methods using various values of the effective length factor, K, with the gusset plate buckling data points from the analyses. Buckling curves were 95

118 created for Joint U10 of I-35W, Joint L2 of BR N and Joint L9 of BR using the three previously described methods and are shown in Figure 4.29 through Figure Joint L5 from BR was excluded from this portion of the study because the geometry of the joint prevented buckling of the gusset plate. Based on the results shown in Figure 4.29, the Thornton method proves to consistently overestimate the buckling capacity of the gusset plate. Similarly the Yoo method also predicts higher buckling capacities than those calculated using the results from the finite element analysis, as shown in Figure Using the information provided by the buckling curves shown in Figure 4.30, it was determined that using the Modified Thornton method, with an effective length factor K equal to 1.0, was a conservative estimate of gusset plate buckling capacity (Wang 2011). There were some cases in which using the Modified Thornton method with K equal to 1.0 proved to be unconservative. When Figure 4.30(c) is examined, there are four cases at the lowest value of L/t where the points fall below the K = 1.0 buckling curve. At this particular plate thickness, inelastic buckling has occurred and so the yield check of the TEP should ostensibly be the governing capacity of the joint. To make sure this is the case, the TEP yield capacity of the compression connection was calculated and compared to the predicted buckling load, as shown in Table 4.6. This shows that the TEP yield capacity does indeed govern and so the Modified Thornton method remains as an appropriately conservative method for determining gusset plate buckling capacity. 96

119 Figure 4.29: Comparison of buckling stress versus effective length from analysis with buckling stress predicted using the Thornton method for (a) Joint U10 from I-35W with Fy = 50ksi, (b) Joint L2 from BR N with Fy = 45ksi and, (c) Joint L9 from BR with Fy = 33ksi 97

120 Figure 4.30: Comparison of buckling stress versus effective length from analysis with buckling stress predicted using the Modified Thornton method for (a) Joint U10 from I-35W with Fy = 50ksi, (b) Joint L2 from BR N with Fy = 45ksi and, (c) Joint L9 from BR with Fy = 33ksi 98

121 Figure 4.31: Comparison of buckling stress versus effective length from analysis with buckling stress predicted using the Yoo method for (a) Joint U10 from I-35W with Fy = 50ksi, (b) Joint L2 from BR N with Fy = 45ksi and, (c) Joint L9 from BR with Fy = 33ksi Table 4.6: Comparison of the TEP yielding capacity and the predicted buckling load using the Modified Thornton method for Joint L9 of BR TEP Yielding Capacity, Pr (k) Predicted Buckling Load Load Case # Pcr (k)

122 Chapter 5: Implementation and Comparison of the TEP with FHWA Procedures 5.1 General The Triage Evaluation Procedure (TEP) involves three basic checks for each joint in a steel truss bridge. These checks include: (i) the onset of gusset plate yielding, (ii) gusset plate buckling where compression members are attached, and (iii) fastener resistance for the connection at each truss member. These checks should be able to conservatively identify gusset plates which may be inadequate and eliminate those that have sufficient capacity from any additional analysis. This chapter details the implementation of the procedure and compares the resulting load ratings with those obtained using to current FHWA evaluation procedures. 5.2 Application of TEP to WSDOT Bridges The TEP was applied to each joint of the three WSDOT bridges described previously to determine rating factors (RF s). Rating factors were calculated using three different methods: (i) per the load and resistance factor rating (LRFR) method in the AASHTO Manual for Bridge Evaluation (AASHTO 2008) referred to the MBE herein, (ii) per the load factor rating (LFR) method in the MBE, and (iii) per the LRFR method in Chapter 13 of the WSDOT Bridge Design Manual (WSDOT 2010). In all cases the HS20 live load described previously was employed. For the LRFR method in the MBE the RF is determined using: MBE LRFR RF MBE LRFR csrn DC DC LL IM LL DW DW (6.2.1) where c is the condition factor, taken as 0.95 here, s is the system factor, taken as 0.9 here, is the LRFD resistance factor, R is the nominal resistance, DC is the components dead load, DW is the n 100

123 wearing surface dead load, LL is the live load, is the load factor for a particular load, and IM is the dynamic effect of the live load taken to be 1.33 here. The live and dead load factors are given in Table 5.1. It should be noted that the MBE permits the LRFR method to be applied at both the strength and service limit states using both inventory and operating load levels. For this purpose, different load factors, as shown in Table 5.1, only the Strength I and Service II limit states are considered here. Even though RF s are calculated for all four combinations of limit state and load level, it is recommended that the Service II limit state be used for the TEP because the yielding check is not a failure mode, but rather is used to predict the onset of yielding in the gusset plate. Additionally, in all cases examined the yielding check always governed over the compression buckling check. Table 5.1: Load factors for load rating with different load rating procedures MBE LRFR Strength I Service II Load Factor Inventory Operating Inventory Operating DC DW LL Load Factor MBE LFR Inventory Operating A A Load Factor BDM LRFR D 1.3 L

124 For the LFR method in the MBE, which is the same as the National Bridge Inventory Rating in the WSDOT Bridge Design Manual (BDM, WSDOT 2006), the rating factor, RF, is calculated as: MBE LFR RF MBE LFR C A1 D A L1 I 2 (6.2.2) where C is the capacity, A 1 is the load factor for dead loads, A 2 is the load factor for live loads, D is the dead load, and L is the live load. I is the dynamic impact factor which is given by: I L (6.2.3) where L is the length in feet of the portion of the span that is loaded to produce the maximum stress in the member with a maximum value of 0.4. The load factors for the inventory and operating load levels for this rating method are given in Table 5.1. Finally, the WSDOT Bridge Design Manual (WSDOT 2006) has a LRFR rating factor, RF, that is taken as: BDM LRFR RF BDM LRFR Rn DD L 1 I L (6.2.4) where φ is the resistance factor per the 1989 AASHTO Guide Specifications for Strength Evaluation of Existing Steel and Concrete Bridges (AASHTO 1989), R is the nominal resistance, D is the dead load, L is the live load, I is the dynamic impact factor which is taken as 0.2 here and γ is the load factor for particular loads which are shown in Table 5.1. It should be noted that the RF is calculated using only the strength limit state and no distinction is made between the inventory and operating load levels. n BDM LRFR Table 5.2 through Table 5.4 show the RF s for each joint on the three WSDOT bridges using the three rating methods described above and the yielding and buckling resistances calculated per the TEP. 102

125 The rivet check is not included here and is discussed in later sections. Joints that had only hangers connected were not included in these ratings. As shown, the TEP results in a number of RF s less than 1.0 using the MBE LRFR rating method at the Strength I limit state under the inventory load level. This result is expected since this is a strength limit state and the basis of the TEP is the onset of gusset plate yielding rather than gusset plate failure. When the RF s are examined for the MBE LRFR Service II limit state at the inventory load level, 3 of the total 35 joints have RF s less than 1.0. This indicates that gusset plates at these joints could be yielding under service load conditions and may require further investigation. These three joints will be discussed in further detail below. At the operating load level and Service limit state for the MBE LRFR rating method none of the joints have RF s less than 1.0, while several joints have RF s less than 1.0 for the Strength I limit state. When the RF s calculated using the MBE LFR method at the inventory load level are examined, the joints that have RF s less than 1.0 are found to be the same as those with RF s less than 1.0 from the MBE LRFR method, Strength I limit state and inventory load level. Further, the RF s from the MBE LFR method are generally larger than those from the MBE LRFR method. Table 5.2 through Table 5.4 also show that no joints have RF s less than 1.0 at the operating load level for the MBE LFR rating method. Finally, for the BDM LRFR method, four joints have RF s less than 1.0, one of which has a value of

126 Table 5.2: Rating Factors for BR N Joints Using the TEP MBE - LRFR Strength I MBE - LRFR Service II MBE - LFR BDM - Joint Inventory Operating Inventory Operating Inventory Operating LRFR ID L L U U2* * Indicates joints where all RFs would be greater 1.0 if compressions chords that are milled-to-bear were neglected. Table 5.3 Rating Factors for BR Joints Using the TEP MBE - LRFR Strength I MBE - LRFR Service II MBE - LFR BDM - Joint Inventory Operating Inventory Operating Inventory Operating LRFR ID L L L L L L L U U U U U U U

127 Table 5.4 Rating Factors for BR Joints Using the TEP MBE - LRFR Strength I MBE - LRFR Service II MBE - LFR BDM - Joint Inventory Operating Inventory Operating Inventory Operating LRFR ID L L L3* L5* L L L L L U2# U3# U U U U U U * Indicates joints where all RFs would be greater 1.0 if compressions chords that are milled-to-bear were neglected. # Indicates joints where all RFs would be greater than 1.0 if chords were neglected due to the splice being well outside the interference zone. As mentioned previously, 3 of the total 35 joints evaluated using the MBE LRFR method at the Service II limit state and inventory load levels had RF s less than 1.0. This indicates that the gusset plates have yielded under these loading conditions. With closer inspection, as described below, it can be shown that due to their unique configurations two of these gusset plates can be assigned RF s greater than 1.0. The third gusset plate may be yielding under these load levels. 105

128 The first connection that was identified as having a RF less than 1.0 using the TEP was Joint L3 from BR , which is shown in Figure 5.1. This joint is located along the bottom chord of the back span portion of the cantilevered truss bridge and so both chords framing into joint are loaded in compression. Figure 5.1(a) also shows the RF s calculated for each connection of the joint using the MBE LRFR method with the Service II limit state and inventory load levels. As this Figure demonstrates, the lowest RF for the joint is due to the connection for chord L3-L4. However, the chord connections were specified as milled-to-bear, as shown in the design drawing in Figure 5.1(b). That is, the ends of both chord members are in direct contact with one another which implies that the gusset plate is not transferring much of their stress. For this joint, only 0.14% of the live load in chord L3-L4 needs to be transferred through bearing in order to have a RF equal to 1.0; which is a very reasonable amount assuming that the bearing can be field verified. Therefore, under similar conditions in other bridges, these types of milled-to-bear connections for compression chords can be neglected using the TEP. Figure 5.1: Joint L3 from BR with (a) RF's calculated using MBE LRFR Service II load combinations under Inventory load levels, and (b) Design drawings of the joint showing milled to bear condition of chord members 106

129 Another joint that was identified as having a RF less than 1.0 using the TEP and the MBE LRFR method with Service II limit state and inventory load levels was Joint U2 from BR , which is shown in Figure 5.2. This joint is located along the top chord of the back span portion of a cantilevered truss bridge and so both chord members are in tension. Figure 5.2 shows that both of the chord connections in this joint have RF s less than 1.0. What makes this joint unique from other joints studied is that the chords are spliced a considerable distance away from the work point and the previously described critical area. Because the chord splice is far offset from the location of the interference of stresses assumed in the derivation of the TEP yield check it can be presumed that this check is overly conservative when applied to Joint U2. This is because the high levels of stress located at the ends of the chord members are well away from the stresses caused by the diagonal and vertical members. Since the stresses due to the chord member loads are not coincident with the stresses due to the other members in the joint, they cannot interact to cause yielding of the gusset plate. 107

130 Figure 5.2: Calculated RF's for Joint U2 of BR using MBE Service II load combinations under inventory load levels and the location of the offset chord splice To investigate these assumptions, a detailed finite element model of Joint U3 from BR was created. Joint U2 was not able to be modeled due to the poor quality of the available shop drawings; however, Joint U3 is similarly configured and so was suitable for modeling. The RF s calculated for the two chord members of Joint U3 were 1.12 and 1.07 for the MBE LRFR method and Service II limit state at the inventory load level. This indicates that this gusset plate is approaching the onset of yielding and so stresses in the critical area should be near yield. These loads were then used in the finite element analysis to investigate the stress state of the gusset plate. Figure 5.3 shows a contour plot of the Von Mises stresses in the gusset plate for Joint U3 under these loads and that the gusset plate has not yet reached its yield stress of 30 ksi. In fact, the maximum Von Mises stress that is achieved is 21.6 ksi located in a region located near the chord splice. The maximum Von Mises stress calculated in the critical area is between 10 and 15 ksi. Therefore, when the chord splice is away from the critical area of the joint it is likely that the TEP yield check will be overly conservative. 108

131 The calculated Whitmore stresses for the chord connections U3-U4 and U3-U2 under these loading conditions is calculated is 12 ksi and 10.9 ksi, respectively. This demonstrates that even though the chords are connected well away from the critical area and so are not subjected to the interference of stresses, even the standard Whitmore stress calculation is unable to predict the maximum stress in the gusset plate. The inability to predict the stress state for these particular chord connections remains an area of research that needs to be pursued. Figure 5.3: ANSYS rendering of the Von Mises stresses for Joint U3 of BR using the MBE LRFR Service II load combination under inventory load levels with chord splice and critical area locations The final joint with a RF less than 1.0 using the MBE LRFR rating method and Service II limit state under the inventory load level is Joint L9 from BR 31-36, as shown in Figure 4.4 (Wang 2011). This joint is located along the lower chord of a cantilevered truss bridge and so the chord member L9-L8 is in compression. The other chord, Member L9-L10, is a zero-force member because it is part of the expansion joint system for the drop-in simple span portion of the bridge (see Section 4.4 for a detailed description of this joint). Upon further examination, this joint has characteristics similar to 109

132 the joint used to derive the TEP yield check. That is, the two diagonal members are approximately orthogonal and the loads are nearly equal in magnitude, but opposite in sign. Therefore, under these conditions if the TEP yield check is giving a RF of less than 1.0 then the gusset plate should be beginning to yield. To confirm this, these loads were inputted into the detailed finite element model of the joint and Von Mises stress contours were plotted, as shown in Figure 5.4 (Wang 2011). This Figure shows that the gusset plate has reached a maximum Von Mises stress of 27 ksi which is approaching the specified yield stress of 33 ksi for the material. This demonstrates that this gusset plate is under considerable stresses which may be a concern for the bridge owners as well as illustrating the inherent conservativeness of the TEP yield check. Figure 5.4: Von Mises stress contours for Joint L9 from BR using loads from MBE LRFR rating method and Service II limit state with inventory load level 110

133 If the aforementioned milled-to-bear joint type is given a RF greater than 1.0, which would be the case given the discussion above, then only two joints are identified as being highly stressed using the MBE LRFR method with the Service II limit state at the inventory load level. 5.3 Comparison with FHWA Load Ratings The RF s computed using the FHWA Guide procedure were calculated using the MBE LRFR Strength I load combination at the inventory load level and were compared to the RF s from the TEP using the Service II load combination at the inventory load level. Table 5.5 through Table 5.7 compare the RF s for the two cases and demonstrate that the TEP applied at service loads is consistently conservative relative to the FHWA Guide procedure applied at strength loads. For joints from BR where the vertical or diagonal members pass through the work point to the top or bottom of the gusset, as shown in Figure 5.1(b) and Figure 5.2, it was not possible to draw unobstructed lines for the vertical and horizontal shear checks in the FHWA Guide. Consequently, the shear checks were not included in those cases. The tables also show the governing limit state from the FHWA Guide procedure. Table 5.5: Rating factors for BR N joints from the TEP with Service II Inventory Loads and the FHWA Guide with Strength I Inventory loads Joint Identification U1 U3 L2 L4 Triage RF FHWA RF FHWA Mode 1 HS VS C GSY 1 GS = Gross Section Yielding, HS = Horizontal Shear, VS = Vertical Shear, BS = Block Shear, C = Compression Buckling 111

134 Table 5.6 Rating factors for BR Joints from the TEP with Service II Inventory Loads and the FHWA Guide with Strength I Inventory loads Joint Identification U2 U4 U6 U8 U10 U11 U13 Triage RF FHWA RF FHWA Mode 1 HS VS HS HS VS VS C Joint Identification L1 L3 L5 L7 L9 L10 L12 Triage RF FHWA RF FHWA Mode 1 HS VS HS C HS VS HS 1 GS = Gross Section Yielding, HS = Horizontal Shear, VS = Vertical Shear, BS = Block Shear, C = Compression Buckling Table 5.7 Rating factors for BR Joints from the TEP with Service II Inventory Loads and the FHWA Guide with Strength I Inventory loads Joint Identification U2 U3 U4 U5 U6 U7 U9 U10 Triage RF FHWA RF FHWA Mode 1 GSY GSY BS GSY GSY BS GSY GSY Joint Identification L1 L2 L3 L5 L6 L7 L8 L9 L11 Triage RF FHWA RF FHWA Mode 1 C C C GSY GSY GSY GSY GSY BS 1 GS = Gross Section Yielding, HS = Horizontal Shear, VS = Vertical Shear, BS = Block Shear, C = Compression Buckling 112

135 The Tables above show that the only joint of the three bridges considered that has an RF of less than 1.0 using the FHWA Guide procedures, Joint L9 from BR 31-36, also has an RF of less than 1.0 using the TEP. Additionally, if the RF s less than 1.0 from the TEP for BR are not considered as they are resulting from compression chords that are milled-to-bear and tension chords with splices outside the interference zone, only Joint L9 has an RF of less than 1.0 from the TEP. Consequently, using the TEP at service loads is both conservative relative to the FHWA Guide approach and is also consistent with the FHWA Guide approach in identifying the same joint as having insufficient capacity at the inventory load levels. 5.4 Load Ratings Including Rivets The RF s calculated above did not include the rivet shear limit state so that the gusset plate checks developed in the TEP could be compared to their FHWA counterparts. Given in the FHWA Guide are recommended rivet shear strengths, as shown in Table 5.8, which are dependent on the age of the bridge under consideration. Of the three bridges considered here the rivet strengths for BR N and BR would be 21 ksi while BR would be assigned rivet strengths of 18 ksi. Given these rivet strengths and considering only the rivet limit state, RF s were then calculated for all of the joints of the three bridges. The resulting RF s are shown in Table 5.9 through Table 5.11 for the MBE LRFR and MBE LFR rating methods. As shown, almost every RF is smaller than the corresponding RF calculated using the gusset plate limit states. Additionally, the majority of rivet RF s are less than 1.0 indicating that the joint is inadequate given the live load conditions. In fact, only one joint has a RF greater 1.0 for the MBE LRFR rating method at the Strength I limit state and inventory load level and only three joints have RFs greater 1.0 for the MBE LFR rating method at the inventory load levels. BR has many rivet RF s less than 1.0 for all rating methods and at all load levels. These RF s would indicate that either many of the rivets on these bridges are inadequate 113

136 and need to be replaced or that the recommended rivet shear strengths are too low. Chapter Chapter 6: reviews rivet data collected from the literature to investigate the possibility of the latter. Table 5.8: Rivet Shear Strengths as Given by the FHWA Guide Rivet Type F (ksi) Constructed prior to 1936 or of unknown origin 18 Constructed after 1936 but of unknown origin 21 ASTM A 502 Grade I 27 ASTM A 502 Grade II 32 Table 5.9 Rating Factors Considering only Rivet Strength for BR N Joints MBE - LRFR Strength I MBE - LRFR Service II MBE - LFR Joint ID Inventory Operating Inventory Operating Inventory Operating L L U U Table 5.10 Rating Factors Considering only Rivet Strength for BR Joints MBE - LRFR Strength I MBE - LRFR Service II MBE - LFR Joint ID Inventory Operating Inventory Operating Inventory Operating L L L L L L L U U U

137 U U U U Table 5.11 Rating Factors Considering only Rivet Strength for BR Joints MBE - LRFR Strength I MBE - LRFR Service II MBE - LFR Joint ID Inventory Operating Inventory Operating Inventory Operating L L L L L L L L L U U U U U U U U

138 Chapter 6: Rivet Ultimate Strength and Effective Rivet Yield 6.1 General As shown in Section 5.4 the check of rivet shear strength governed the capacity of nearly every joint that was load rated on the three WSDOT bridges and resulted in many RF s less than 1.0 indicating the likely need for rivet replacement. Such a result made it necessary to review past research on the strength of riveted joints since these bridges had not had visible rivet problems when field inspected. This chapter explores earlier research on the strength of riveted joints and gives recommendations for appropriate rivet resistances. Each study is briefly reviewed and analysis of rivet strength data is presented in the last section of this chapter. 6.2 Ultimate Rivet Shear Strengths Table 6.1 shows the collected values for rivet shear strengths obtained from the experimental research programs described above. The rivet shear strength values in this Table are from tests where rivet shear failure was the ultimate failure mechanism of the joint. Tests where plate failure occurred were not included in this data. The mean and standard deviations of the collected data show that the ultimate shear strengths given by the FHWA Guide, and shown in Table 5.8, are substantially smaller than the values found in these reports. It should be noted that the values given in the FHWA Guide do include a resistance factor, but even with the assumption of the resistance factor, φ, equal to 0.75, a typical value when ultimate strengths are used, the given values are still considerably conservative. Table 6.1 also shows the ratio of the mean+1 standard deviation shear stress divided by the ultimate tensile stress of the rivet material. As shown, the latter data indicates that Equation (2.9) is a reasonably conservative relationship between ultimate rivet shear strength and tensile strength. 116

139 Test Description Table 6.1: Summary of ultimate rivet shear strength data Material Rivet Tensile Properties (ksi) F y F u # of Tests Mean τ u (ksi) Std Dev. (ksi) (Mean τ u - Std Dev.)/F u (ksi) AREMA (1904) OH Steel Talbot et al. (1911) Woodruff et al. (1939) Wilson et al. (1940) Munse et al.(1956) Nickel Steel Cr-Ni Steel Carbon Steel Mn Steel Low Alloy A Low Alloy B Low Alloy C ASTM A Effective Rivet Yield (ERY) The concept of ERY was introduced by Davis et al. (1939) as a method for describing the point of rivet yield for a riveted connection by utilizing the force-displacement. Figure 6.1 shows a typical rivet shear stress-joint set plot for a riveted joint which has been divided into four different stages. Stage I is the region where the load is transferred from one plate to the other via friction. Stage I ends when the load is sufficient to cause movement of the joint as a whole via slip at the shear plane. Stage II is characterized as the region of slip deformation where the increase in strength is small and the joint set is relatively large. Stage III is characterized by bearing of the rivets on their holes with all material behaving essentially elastically. Finally, Stage IV begins when yielding initiates in the plates, rivets, or both and joint set again increases more rapidly with load. For over-riveted joints yielding occurs in plates, with under-riveted joints yielding occurs in rivets (Davis et al. 1939). The ERY is defined as the rivet shear stress where the rate of increase of joint set with respect to rivet shear is twice that at the beginning of Stage III. 117

140 Figure 6.1: Rivet shear stress-joint set plot for a typical riveted joint under axial load that has been divided into four stages The ERY was calculated for all joints where the rivet shear stress-joint set plots were available. This was accomplished using the following steps. First, the plots were scanned from the research reports and digitized. Next, the Stage III region was identified manually and the slope at the beginning of Stage III was calculated. Then, the point along the curve where the slope became ½ of the initial Stage III slope was found and defined as. Figure 6.2 provides a visual representation of this process. Table 6.2 shows the results for mean ERY from previously described test programs. 118

141 Figure 6.2: ERY determined using rivet shear stress-joint set plot Table 6.2: ERY results from rivet tests Test Description AREMA (1904) Talbot et al. (1911) Woodruff et al.(1939) Wilson et al. (1940) Material # of Tests Mean ERY (ksi) Std Dev. (ksi) (Mean ERY- Std Dev) (ksi) (Mean ERY-Std Dev)/F y FHWA Recommended Strength OH Steel Nickel Steel Cr-Ni Steel Carbon Steel Mn Steel Low Alloy A Low Alloy B Low Alloy C

142 Examining the results from the ERY calculations it appears that the FHWA Guide recommended rivet strengths more closely matches the initiation of rivet yield then it does the ultimate rivet shear strength. Thus, it would be more appropriate to use the FHWA recommended values when checking the rivets under service load levels rather than strength load levels. 6.4 Rivet RF s Using ERY and Revised Ultimate Shear Strengths Recently there has been discussion about the recommended rivet shear strengths given in the FHWA Guide. It is clear that these values are conservative with respect to the data given in the test programs reviewed in this Chapter. In light of the fact that almost every joint would need to have some, if not all, of the rivets replaced if the current strength recommendations are used, internal discussions at the FHWA have proposed using revised rivet strengths, as shown in Table 6.3 (C.W. Roeder, personal communication, December 5, 2010). Using these revised strengths, RF s were calculated, considering only the rivets, using the MBE LRFR Strength I and Service II limit states at both the Inventory and Operating load levels. These results are shown in Table 6.4 through Table 6.6. Looking at these results it is clear that using these revised rivet strengths dramatically decreases the number of joints with RF less than 1.0. In fact, only two joints have RF less than 1.0 using the MBE LRFR Strength I limit state at Inventory load levels. Table 6.3: Proposed FHWA Guide rivet strength revisions Rivet Type F (ksi) Rivets of unknown origin 27 Documentable C content > 0.18% or ASTM A 502 Grade I ASTM A 502 Grade II

143 Table 6.4: Rating Factors considering only revised rivet strengths for BR N Joints MBE - LRFR Strength I MBE - LRFR Service II Joint ID Inventory Operating Inventory Operating L L U U Table 6.5: Rating Factors considering only revised rivet strengths for BR Joints MBE - LRFR Strength I MBE - LRFR Service II Joint ID Inventory Operating Inventory Operating L L L L L L L U U U U U U U

144 Table 6.6: Rating Factors considering only revised rivet strengths for BR Joints MBE - LRFR Strength I MBE - LRFR Service II Joint ID Inventory Operating Inventory Operating L L L L L L L L L U U U U U U U U As mentioned previously, a conservative estimate of the ultimate shear strength of a rivet is given by u 0.75F. In the case where a bridge has a number of joints with rivet RF s less than 1.0, it u might be advantageous for the bridge owner to remove a number of rivets from the bridge and perform tests to determine their ultimate tensile strength, F u. Using this value the ultimate rivet shear strength could be determined and then used to recalculate the rivet RF s. Using this notion, RF s for the three WSDOT bridges were calculated using ultimate rivet strengths calculated from 122

145 rivet tensile strength data from test programs of a similar age. Table 6.7 shows the ultimate rivet strength used to calculate the rivet RF s using the MBE LRFR Strength I limit state under Inventory and Operating load levels. In this case φ was assumed to be The rivet RF s calculated using these values are shown in Table 6.8 through Table Examining these results, only one joint has a RF less than 1.0 under the Inventory load level using this method of determining ultimate rivet strengths. Table 6.7: Rivet ultimate shear strength calculated for the three WSDOT bridges using rivet test program data of a similar age Bridge ID BR N Year Constructed Rivet Test Program of a Similar Age Rivet Material Tensile Strength, F u (ksi) 1949 Munse et al. (1956) BR Munse et al. (1956) BR Woodruff et al. (1939) φf n (ksi) Table 6.8: Rating Factors considering only rivet strengths based on F u for BR N Joints MBE - LRFR Strength I Joint ID Inventory Operating L L U U Table 6.9 Rating Factors considering only rivet strengths based on F u for BR Joints MBE - LRFR Strength I Joint ID Inventory Operating L L L

146 L L L L U U U U U U U Table 6.10 Rating Factors considering only rivet strengths based on F u for BR Joints MBE - LRFR Strength I Joint ID Inventory Operating L L L L L L L L L U U U U U U U U

147 In a similar fashion, ERY strength values could be determined by the bridge owner using material properties of rivets. Looking at the values in Table 6.2, an appropriate method for determining ERY as a function of the rivet material yield strength, F y, is given by: For bridges constructed prior 1930 ERY 0. 5F (1.1.1) y For bridges constructed after 1930 ERY 0. 7F (1.1.2) y The rivet material yield strengths were taken from the same test programs shown in Table 6.7 and then ERY strengths were calculated, as shown in Table Using these ERY strengths, rivet RF s for the three WSDOT bridges were calculated using the MBE LRFR Service II limit state under Inventory and Operating load levels and are shown in Table 6.12 through Table It should be noted that the value used for φ was 0.90; a value typically used for the yield strength of ductile materials. Looking at these results, 21 of the joints have RF s less than 1.0 under the Inventory load level compared to only three at Operating load levels. Using ERY strength results in more RF s less than 1.0 than if the results shown in the FHWA Guide are used (see Table 5.9 through Table 5.11). Table 6.11: ERY values calculated for the three WSDOT bridges using rivet test program data of a similar age Bridge ID BR N Year Constructed Rivet Test Program of a Similar Age Rivet Material Tensile Yield Strength, F y (ksi) 1949 Munse et al. (1956) BR Munse et al. (1956) BR φery (ksi) 1930 Woodruff et al. (1939)

148 Table 6.12: Rating factors considering only rivet strengths based on ERY for BR N Joints MBE - LRFR Service II Joint ID Inventory Operating L L U U Table 6.13: Rating Factors considering only rivet strengths based on ERY for BR N Joints MBE - LRFR Service II Joint ID Inventory Operating L L L L L L L U U U U U U U

149 Table 6.14: Rating Factors considering only rivet strengths based on ERY for BR Joints MBE - LRFR Service II Joint ID Inventory Operating L L L L L L L L L U U U U U U U U

150 6.5 Effect of Joint Parameters on Rivet Strength Two parameters were investigated to explore their impact on rivet ultimate strength and ERY were rivet grip, L, and connection length, L, as shown in Figure 6.3. These parameters were selected g c because previous studies (Munse et al. 1956) have indicated they may have an impact on joint strength. Figure 6.3: Example of (a) rivet grip length, and (b) connection length To compare the results from the different tests, the rivet strengths and connection parameters were normalized. For instance, ERY was normalized to the tensile yield strength of the rivet material, F, the ultimate rivet shear strength, V u, was normalized to the ultimate tensile strength of the material, F, and the grip length and connection length were normalized to the diameter of the u rivet, D. Figure 6.4 through Figure 6.10 show the relationship between rivet ultimate shear r strength and grip length. Figure 6.11 through Figure 6.17 show the relationship between rivet ultimate shear strength and connection length. Figure 6.18 through Figure 6.25 show the relationship between ERY and rivet grip length. Figure 6.26 through Figure 6.31 show the relationship between ERY and connection length. y 128

151 Examining the results shown in Figure 6.4, it appears that there is a relationship between rivet grip length and the ultimate shear strength. While there is a significant amount of scatter in the data, there is a trend that shows that for longer rivet grip lengths, lower ultimate shear strengths can be expected. Looking at the individual test program comparisons, a similar trend is shown; although for some of the programs this relationship is not as strong. When Figure 6.11 is examined, for values of L / 30 it seems that there is some relationship c D r between connection length and ultimate rivet shear strength whereby longer connections have lower ultimate shear strengths. For the range of 30 L / D 80 there is also a similar downward trend between the two parameters. When data is combined, however, the linear regression analysis indicates little relationship. It should be noted that the number of test programs with longer connection lengths were far fewer than those with short connection lengths, thus resulting in fewer data points. When the individual test program comparisons are examined, most demonstrate this downward trend. It should be noted, that for the Wilson et al (1941) test program, all of the joints tested had the same L / D ratio and so linear regression analysis was not possible. c r c r The results shown in Figure 6.18 demonstrate that there is a correlation between the rivet grip length and the ERY strength. While there is significant scatter in the data, there is a trend that shows that rivets with longer grip lengths typically have lower ERY strengths. The results from the individual test program comparisons also show this trend; although for some of the programs no relationship could be found between the two parameters. When the results in Figure 6.25 are examined, it appears that there is little relationship between connection length and ERY strength. While it might be expected that a trend similar to the relationship between connection length and ultimate shear strength would be observed, there is just too much variability in the data to support this claim. 129

152 The reason that there is a correlation between L c / Dr and V u / Fu is due to the way Vu is determined. When these connections fail it is typically observed that outermost rivets in the connection fail first. This implies that these rivets are more heavily loaded than the rivets in the interior of the connection; a phenomenon typically called shear lag. Even though the most extreme rivets fail first, the ultimate shear strength of the joint is calculated using the assumption that all of the rivets share the load equally. Therefore, the longer the joint the more rivets there are to divide the breaking load by and so the ultimate rivet shear stress decreases. The reason that there is no relation between L c / Dr and ERY / Fy is because at the point of ERY the deformations in the joint are typically small relative to the deformations at ultimate load. Because of this the shear lag effect has not occurred and so the assumption that all of the rivets in the connection share equal load is justified. This is why there is no trend between the length of the connection and the ERY strength of a riveted connection. The effects of rivet grip on the ERY and ultimate shear strength of a riveted joint can attributed to how a rivet deforms when the grip length increases. For rivets with short grip lengths the deformation mode can be described as a true shear deformation. That is, there is little rotation of the rivet head with respect to the rivet body. When rivet grip length increases, however, the rivet head can rotate substantially which is akin to a bending deformation. As the rivet head rotates, tensile stresses are introduced thus producing a combined shear and tension condition. This combined shear and tension stress state leads to lower ultimate strengths, as documented in Munse et al. (1956). This difference in deformation modes is the reason that as rivet grip lengths increase both the ERY and ultimate shear strength decrease. 130

153 Figure 6.4: Comparison between ultimate rivet shear strength and rivet grip for all tests Figure 6.5: Comparison between ultimate rivet shear strength and rivet grip from AREMA (1904) 131

154 Figure 6.6: Comparison between ultimate rivet shear strength and rivet grip for Cr-Ni steel from Talbot et al. (1911) Figure 6.7: Comparison between ultimate rivet shear strength and rivet grip for Ni steel from Talbot et al. (1911) 132

155 Figure 6.8: Comparison between ultimate rivet shear strength and rivet grip from Wilson et al. (1941) Figure 6.9: Comparison between ultimate rivet shear strength and rivet grip for C steel from Davis et al. (1941) 133

156 Figure 6.10: Comparison between ultimate rivet shear strength and rivet grip for Mn steel from Davis et al. (1941) Figure 6.11: Comparison between ultimate rivet shear strength and connection length for all tests 134

157 Figure 6.12: Comparison between ultimate rivet shear strength and connection length from AREMA (1904) Figure 6.13: Comparison between ultimate rivet shear strength and connection length for Cr-Ni steel from Talbot et al. (1911) 135

158 Figure 6.14: Comparison between ultimate rivet shear strength and connection length for Ni steel from Talbot et al. (1911) Figure 6.15: Comparison between ultimate rivet shear strength and connection length from Wilson et al. (1911) 136

159 Figure 6.16: Comparison between ultimate rivet shear strength and connection length for C steel from Davis et al. (1939) Figure 6.17: Comparison between ultimate rivet shear strength and connection length for Mn steel from Davis et al. (1939) 137

160 Figure 6.18: Comparison between ERY strength and rivet grip for all tests Figure 6.19: Comparison between ERY strength and rivet grip from AREMA (1904) 138

161 Figure 6.20: Comparison between ERY strength and rivet grip for Cr-Ni steel from Talbot et al. (1911) Figure 6.21: Comparison between ERY strength and rivet grip for Ni steel from Talbot et al. (1911) 139

162 Figure 6.22: Comparison between ERY strength and rivet grip from Wilson et al. (1941) Figure 6.23: Comparison between ERY strength and rivet grip for C steel from Davis et al. (1939) 140

163 Figure 6.24: Comparison between ERY strength and rivet grip for Mn steel from Davis et al. (1939) Figure 6.25: Comparison between ERY strength and connection length for all tests 141

164 Figure 6.26: Comparison between ERY strength and connection length from AREMA (1904) Figure 6.27: Comparison between ERY strength and connection length for Cr-Ni steel from Talbot et al. (1911) 142

165 Figure 6.28: Comparison between ERY strength and connection length for Ni steel from Talbot et al. (1911) Figure 6.29: Comparison between ERY strength and connection length from Wilson et al. (1941) 143

166 Figure 6.30: Comparison between ERY strength and connection length for C steel from Davis et al. (1941) Figure 6.31: Comparison between ERY strength and connection length for Mn steel from Davis et al. (1941) 144

167 6.6 Summary Based on the results it seems that the values recommended by the FHWA as ultimate rivet strengths would be more appropriately used as values for ERY. Furthermore, the ultimate shear strength of a rivet given by Equation (2.17.2) seems to be an appropriately conservative estimate. Additionally, it has been demonstrated that as rivet grip length and connection length are increased, reductions in the ultimate rivet shear strength should be made. Similarly, ERY strengths should be reduced as rivet grip length increases, however, no relationship between ERY strength and connection length could be found. 145

168 Chapter 7: Summary, Conclusions and Recommendations 7.1 Summary The collapse of the steel truss I-35W Mississippi River Bridge in Minneapolis, Minnesota was attributed to a number of the gusset plates being significantly overstressed (Ocel and Wright 2008). In response to this the FHWA released a gusset plate evaluation guide which contain procedures that are likely to require significant resources for the bridge owners, namely state DOT s. Based on the service record of steel truss bridges in the US it can be assumed that the number of overstressed gusset plate is small. The TEP was developed so that gusset plate connections could be efficiently, yet conservatively, evaluated while identifying those that may be a concern. With this goal in mind, different aspects of gusset plate behavior were studied to help develop this procedure. The first behavior studied was the yielding behavior of gusset plate connections. The currently recommended procedures in the FHWA Guide may not identify all gusset plates that may be yielding under service loads. Analysis results indicated that a complex interaction of stresses is generated in gusset plates by the connecting members. This interaction can initiate gusset plate yielding when the uniaxial stresses on Whitmore sections associated with those connecting members are well below yield. Simple mechanics were used to develop a conservative and considerably simpler process for identifying gusset plates that may be yielding by calculating the Whitmore stress for each connecting member and ensuring that it is less than F / 3. Detailed finite element analysis indicated this method conservatively predicted the onset of gusset plate yielding and was consistently conservative relative to the procedures in the FHWA Guide. y Gusset plate buckling was also investigated using the detailed finite models developed in this study. It was found that gusset plate buckling did not occur prior to gusset plate yielding in any of the 146

169 connections studied at their design thicknesses. When buckling may be a concern, the Modified Thornton Method of evaluating the gusset plate unbraced length and compressive stress, along with an effective length factor of 1.0, was found to be conservative when used with the AISC buckling equations. When applied to three bridges in Washington State, the TEP was found to be easy to implement and appropriately conservative. It resulted in rating factors (RF s) that were conservative relative to the procedures in the FHWA Guide. When applied at service limit states or operating load levels the TEP identified few joints as needing further investigation (i.e., having an RF greater than 1.0). When the rivet strengths recommended in the FHWA Guide were employed to calculate RF s using strength load combinations, it was shown that many joints of the three bridges considered had RF s less than 1.0. In light of this a review of past tests has indicated that these recommended rivet strengths may be overly conservative. Based on the data from past tests programs, ultimate rivet shear strength, σ u, can be conservatively estimated using 0.75F, where Fu is the ultimate tensile strength of the rivet material. u u Additionally, the concept of Effective Rivet Yield (ERY) was investigated as a more appropriate limit state when considering service load combinations (Davis et al. 1939). It was shown that ERY could also be calculated using the tensile yield strength of the rivet material, F y, whereby for bridges constructed before 1930, ERY 0. 5Fy and for bridges constructed after 1930, ERY 0. 7Fy. Parameters such as rivet grip length and connection length (see Figure 6.3) were investigated to determine the effects they have on rivet ultimate shear strength and ERY strength. It was shown that reductions in rivet ultimate shear strength and ERY strength should be made for increasing rivet 147

170 grip lengths. Additionally, reductions in ultimate rivet shear strength should be made for longer connections, however, no such reductions are necessary for ERY strength. 7.2 Conclusions The TEP is an efficient, yet conservative, method for identifying gusset plates in steel truss bridges that may be overstressed. The yield check of the procedure is able to consistently predict the onset of gusset plate yielding under service load combinations. While gusset plate yielding was observed well before buckling, the procedure is also able to identify gusset plates where buckling may be a concern. The rivet check in the procedure is identical to the check in the FHWA Guide, however, the recommended rivet strengths given in this guide are overly conservative. It would be more advantageous for bridge owner to use rivet material strengths from the bridge in question to determine either rivet ultimate shear strength or ERY strength. 7.3 Recommendations for Further Research This thesis has demonstrated that the TEP is a useful tool in rapidly evaluating gusset plate in steel truss bridges. However, additional research is needed to address some of the issues raised during this investigation. The list below highlights some of the more critical research needs: Development a refined evaluation procedure for use on those joints that are identified as likely yielding under service loads in the TEP. The refined procedure should eliminate some of the conservative assumptions used to develop the yield check of the TEP. Assess the impact of layered gusset plates on stress distributions and gusset buckling Study of the effect of corrosion in the critical regions of the gusset plate where the stresses generated from connecting elements interfere with each other. Investigate the impact of fastener response on gusset plate stress distributions in the detailed finite element models 148

171 Compare strength of rivets that have been in service to historical test data Past rivet test programs typically only investigated relatively simple joint configurations. In reality gusset plate connections have a number of different elements (e.g. wind bracing gusset plates, splice plates, etc.) that connect the members framing into the joint. Rivet behavior for these complex joints need to be investigated further through an experimental test program. 149

172 Chapter 8: References AASHTO (2007). LRFD Bridge Design Specifications, American Association of State Highway and Transportation Officials. AASHTO (2008), Manual for Bridge Evaluation, 1 st Edition, American Association of State Highway and Transportation Officials. AISC (2002), Specifications for Structural Steel Buildings, American Institute of Steel Construction. ANSYS (2008), ANSYS Release 11 Reference Manual, ANSYS, Inc. AREMA (1904). Tests of Riveted Joints, American Railway Engineering and Maintenanceof-Way Association, Proceedings, Vol. 6, p ASTM (1924). ASTM A7 Standard Specifications for Structural Steel for Bridges. American Society for Testing and Materials. ASTM (1939). ASTM A7-39 Standard Specifications for Structural Steel for Buildings and Bridges. American Society for Testing and Materials. ASTM (1946). ASTM A94-46 Standard Specifications for Structural Silicon Steel. American Society for Testing and Materials. Bjorhovde, R., and Chakrabarti, S. K., (1985). Test of Full Size Gusset Plate Connections, ASCE, Journal of Structural Engineering, Vol. 111, No. 3, p Brown, V.L.S., (1998) Stability of Gusseted Connections in Steel Structures, Doctoral Dissertation, University of Delaware CSI (2008). SAP2000 Linear and Nonlinear Static and Dynamic Analysis and Design of Three- Dimensional Structures, Reference Manual, Computers and Structures, Inc. Davis, R.E., Woodruff, G.B., and Davis, H.E., (1939) Tension Tests of Large Riveted Joints, ASCE, Transaction of the American Society of Civil Engineers, Vol. 105, No. 2084, p

173 FHWA (2009). Load Rating Guidance and Examples for Bolted and Riveted Gusset Plates in Truss Bridges. Publication No. FHWA-IF , Federal Highway Administration. Hardash, S.G. and Bjorhovde, R., (1985) New Design Criteria for Gusset Plate in Tension, AISC, Engineering Journal, Vol. 22, No. 2, p77-94 Kulak, G.L., Fisher, J.W., and Struik, J.H.A., (1987) Guide to Design Criteria for Bolted and Riveted Joints. New York, NY. Munse, W.H., and Cox, H.L. (1956) The Static Strength of Rivets Subjected to Combined Tension and Shear, University of Illinois, Bulletins of the Engineering Experiment Station, No Ocel, J.M. and Wright, W.J. (2008). Finite Element Modeling of I-35 Bridge Collapse, Final Report, Turner-Fairbank Highway Research Center Report, Federal Highway Administration. Roeder, C.W., Lehman, D.E., and Yoo, J.H., (2005) "Improved Seismic Design of Steel Frame Connections," International Journal of Steel Structures, Korean Society of Steel Construction, Seoul, Korea, Vol. 5, No. 2, pgs Sheng, N., Yam, M. C. H., and Lu, V.P., (2002) Analytical Investigation and the Design of the Compressive Strength of Steel Gusset Plate Connections, Journal of Constructional Steel Research, v 58, p Talbot, A.N. and Moore, H.F. (1911) Tests of Nickel-Steel Riveted Joints, University of Illinois, Bulletins of the Engineering Experiment Station, Vol. 7, No. 49, p1-53. Thornton, W.A., (1984) Bracing Connections for Heavy Construction, AISC, Engineering Journal, Vol. 21, No 3, p WSDOT (2010). Bridge Design Manual LRFD, Washington State Department of Transportation. Whitmore, R.E., (1952) Experimental Investigation of Stresses in Gusset Plates, Bulletin NO. 16, Engineering experiment station, University of Tennessee. 151

174 Wilson, W.M., Bruckner, W.H., and McCrackin, T.H., (1942) Tests of Riveted and Welded Joints in Low-Alloy Structural Steels, University of Illinois, Bulletins of the Engineering Experiment Station, No Yam, M.C.H. (1994). Compressive Behavior and Strength of Steel Gusset Plate Connections. Doctoral Dissertation, University of Alberta. Yam, M. C. H, and Cheng, J. J. R., (2002) Behavior and Design of Gusset Plate Connections in Compression, Journal of Constructional Steel Research, v 58, n 5-8, p Yoo, J.H. (2006). Analytical Investigation on the Seismic Performance of Special Concentrically Braced Frames, Ph.D. Dissertation, University of Washington. Yoo, J.H., Roeder, C.W., and Lehman, D.E., (2008) "FEM Simulation and Failure Analysis of Special Concentrically Braced Frame Tests," ASCE, Journal of Structural Engineering, Vol.134, No. 6, Reston, VA, pgs

175 Chapter 9: Appendix This section contains a description of and instructions for using the TEP spreadsheet that has been provided to WSDOT. For each joint a careful assessment of the geometry is necessary as this is the key input for the spreadsheet. The first step in using the TEP spreadsheet is the input of the basic information for the gusset plate being evaluated. Cells that are highlighted in blue represent user input cells while cells highlighted in red represent cells that are inactive. The user begins at the top of the spreadsheet directly under the Gusset Plate Inputs & Summary cell. Here information such as the user s name, the company, date and gusset plate ID and the bridge to which the gusset belongs. Additionally there is a drop down tab labeled Include Rivets?. This is here to toggle on or off the rivet evaluation portion of the gusset plate check. At the point when an appropriate rivet strength is chosen for the bridge, the rivet evaluation will be included in the calculated rating factors. Until then, the rivets can be left out. The other tab included in this table is the Number of Connections cell. Here the user utilizes the drop down menu to input the number of connections associated with the gusset plate being evaluated. This appropriately highlights the correct number of tables that need to be filled out below. The remaining cells that need to be filled out are the values associated with the condition factor, c, and the redundancy factor, s. The aforementioned user inputs cells are shown in Figure 9.1. Figure 9.1: First input cells in the TEP spreadsheet The next table that needs filled out by the user is the LL Input & RF Summary table. Here the user inputs the different load cases for which gusset plate connection will be evaluated. For each load case, information such as truck type, live load factors, impact factors and rating methods are 153

176 inputted directly or selected from a drop down menu. The three cells titled Minimum RF, Controlling Connection ID and Controlling Resistance Type will be populated once all of the information for each connection is inputted in the lower sections of the spreadsheet. These cells provide an executive summary of the controlling RF, the connection that causes this RF as well as the resistance type. A sample of this table can be seen in Figure 9.2. Figure 9.2: LL Input and RF Summary Table in the TEP spreadsheet The next table that needs to be completed by the user is the Material & Dimension table. Here the user inputs the yield strengths for the gusset plates and splice plates as well as the ultimate strength of the rivets. The rivet strength cell will be inactive depending on the selection of the Include Rivets? cell as discussed before. Additionally there are inputs for the number of main gusset plates as well as their thicknesses. A sample of the Material & Dimension table is shown in Figure 9.3. Figure 9.3: Gusset plate property input in the TEP spreadsheet Once the user has finished inputting the appropriate values into the preceding tables, evaluation of each connection in the gusset plate can begin. This starts by using the Connection Information table under the Triage Procedure Connection Inputs section shown in Figure

177 Figure 9.4: Connection information input in the TEP spreadsheet The first input is the Connection ID cell. As an example the connection going from gusset L1 to gusset L0 is being evaluated. Next the user selects whether the connection corresponds to a chord or web member using the dropdown menu in the Chord or Web? cell. Next the user uses the drop down menus in the Splice PL s? and Wind Bracing GP? cells which will trigger the inclusion of the appropriate areas for the triage procedure calculation. The next cell, Comp. or Tension?, triggers the inclusion of the buckling check which will be discussed later in these instructions. The final cell in the row is titled Milled to Bear? This cell can only be triggered when the connection corresponds with a chord that is in compression. If Y is selected for this cell than the evaluation of this connection of the gusset plate can be stopped because the member is milled to bear and thus the triage approach does not apply, buckling is not possible and the rivets are provide little to no load transfer. If this is the case, than the user can proceed directly to the next connection, otherwise if N is selected, than the evaluation proceeds as normal. The next step in the Triage Procedure Connection Inputs section is calculate the yielding resistance of the gusset plate connection. This starts by inputting the basic geometry of the connection itself. Parameters such as connection width,, connection length,, and edge length,, are inputted into their respective cells. It should be noted that the edge length cell will only be active for chord member connections, otherwise this cell will be shaded red. Next the user inputs the information associated with any splice plates used in the connection. Parameters like splice identification, plate width and thickness are inputted into the Splice ID,, 155

178 and cells, respectively. These splice plate input cells will only be activated if the user has inputted Y in the Splice PL s cell, as previously described. Finally the user inputs parameters associated with any wind bracing gusset plates into the Wind Brace GP Dimensions table, given that they have trigger this table by inputting Y in the Wind Bracing GP cell. Here information such as brace identification, connection width, connection length, edge distance and wind plate thickness are inputted into the appropriate cells. Now that all of the pertinent information for the yielding portion of the TEP check have been completed, a resistance,, has been calculated for this connection and is displayed at the end of the section. A sample of the yielding calculation for a gusset plate connection is shown in Figure 9.6 The next section in the connection check is the Buckling Resistance Inputs section, shown below. Please note that this section is only triggered for members in compression that are not milled to bear. Here the only main user input is the centroidal buckling length in the Centroidal Length, L_cnt cell. If the user so desires, the recommended values for the compression resistance factor, c, and the effective length factor, K, can be changed as well, but the use of the default values is recommended. The rest of the cells show the values needed calculate the buckling resistance value,. A sample calculation for buckling resistance is shown in Figure

179 Figure 9.5: TEP yield check in the TEP spreadsheet Figure 9.6: Buckling check in the TEP spreadsheet The next section in the connection evaluation is the Rivet Resistance Inputs section shown below. This section is only triggered when the user selects Y in the Include Rivets? cell, as discussed previously, otherwise it remains inactive. Here the user inputs the diameter of the rivets into the Rivet Diameter,D_r cell as well as the number single shear and double shear rivets into the # of Single Shear Rivets, nss and # of Double Shear Rivets, nds cells respectively. Using these inputs, the rivet resistance, Pr, is calculated as shown in Figure 9.7. Figure 9.7: Rivet check in the TEP spreadsheet 157

180 Now that all of the pertinent resistances for the connection in question have been calculated, the user then moves on to the Rating Factors section of the spreadsheet. At the top of this section there are two cells, shown in Figure 9.7, which show the controlling resistance in kips as well as the corresponding type of resistance. Note that is the connection is milled to bear, than these cells will be highlighted yellow and Milled to Bear will be written inside. Figure 9.8: Controlling resistance in the TEP spreadsheet. Next, the user inputs the appropriate values for the dead load factors and loads for LFR and LRFR rating methods. An example of these tables is shown in Figure 9.9. Figure 9.9: Dead and live load factor inputs in the TEP spreadsheet Next the user moves onto the LL Input and RF Summary portion of the table. Here all of the information entered in the LL Input & RF Summary table has been migrated down and is shown merely as a reminder of all the load cases for which the connection will be evaluated. The only user input in this table is the live load that the connection experiences for each load case. This live load, as well as the previously inputted dead loads, is used to calculate RF s for each resistance type for the connection in question. The resistance type that produces the lowest RF s is the controlling resistance and the RF s it produces are highlighted. A sample of this table is shown in Figure

181 Figure 9.10: Rating factor summary table in the TEP spreadsheet When the user completes the Rating Factor section than evaluation of this particular connection is complete and the process repeats itself for each connection in the gusset plate. Once this is complete the user then scrolls to the very top of the spreadsheet to find that the remainder of the LL Input & RF Summary table has been populated and that the executive summary of this particular gusset plate is complete. When the user prints the spreadsheet, the executive summary is printed separately followed a separate page for each individual connection. A sample of the executive summary is shown in Figure

182 Figure 9.11 Executive summary table in the TEP spreadsheet 160