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37 CHAPTER 2. RESEARCH APPROACH REVIEW OF BRIDGE PLANS The plans for 20 different truss bridges were reviewed to help the research team understand the range of designs that might be encountered in the rating process to help guide the research. The findings from this process can be found in greater detail in Appendix A. As a summary, the plans were from eight different states were designed between the years 1929 and 1990, and encompassed a variety of span arrangements and lengths. Some important points that helped to guide the research project were that the overwhelming majority of gusset plates were between 0.500 and 0.938 inches thick while none were observed to be thinner than 0.375 inches. Finally, all connections used either 7/8 or 1 inch diameter fasteners that were either rivets or high-strength bolts. It also became clear that there is no such gusset plate that can be termed as âtypical.â There are numerous variations of geometry, material properties, and force combinations evident in the large gusset plates on the bridges described in Appendix A. Such variations make it impossible to arrive at reasonable conclusions on gusset plate resistance based purely on physical tests. The numbers of tests needed to accomplish this task would be prohibitively expensive. The only viable alternative is to develop robust analytical models that can be used both to explore many more configurations than is possible to test in the laboratory and to assess how independent checks for failure modes can be developed. EXPERIMENTAL PROGRAM Load Frame For successful completion of the project, a unique load frame had to be designed that could load a gusset plate connection to failure. A detailed description of the load frame and its capabilities are further described in Appendix B. Data Systems To capture the variety and magnitude of data required to meet the projectâs objectives, innovative measurement systems that transcend conventional practices were employed during the gusset plate testing. Typically, experiments of this type utilize a combination of LVDTs and strain gauges (single axis or rosettes) to measure displacements and strains. This combination works well when the directions of principal strains and locations of maximum deformations can be reliably anticipated. However, the strain fields within a gusset plate are so complex that an impractical number of strain gauges would be needed to characterize that strain distribution. In addition, the displacement patterns of the gusset plates in three dimensions (i.e., buckled shapes) are difficult to anticipate and thus would also require a large number of deformation sensors to
38 be properly characterized. For this experiment, optical techniques capable of full-field rather than discrete measurements were used to monitor each of the gusset plates. Photostress Camera Each test will consider a pair of gusset plates. During testing, one gusset of the pair will be monitored with a GFP1400 photostress camera furnished by Stress Photonics capable of capturing the full strain field of the gusset plate. The system involves coating the gusset with a tinted epoxy that has certain birefringent characteristics. In this case, stress applied to the epoxy causes a phase shift of the light components transmitted through the epoxy. The phase shift is a circular function expressed in terms of fringes. To maintain elastic superposition principles, this camera and its associated post-processing software recommends keeping the epoxy strains within 1/3 of the first fringe where the circular function is approximately linear. If a certain strain capacity is needed, only the thickness of the coating can be altered to meet this requirement. For the gusset plate experiments, the optimal coating thickness is between 10 and 15 mils yielding a maximum shear strain capacity of ~2000ïï¥ (this correlates to a uniaxial strain of approximately 1500ïï¥). The trade-off with reducing the coating thickness is a decrease in the strain resolution, but this coating thickness should provide approximately a 30ïï¥ resolution. The photostress camera by itself is only able to resolve 2/3 of the entire strain tensor. It is able to determine the diameter of the Mohrâs Circle and direction to the first principal strain, but cannot distinguish the center location of the Circle. The most useful data output by the camera system software is the Maximum Shear Strain contours which is the difference between the two principal strains (i.e., the diameter of Mohrâs Circle). Data collected from the photostress camera for each specimen is presented in Appendix E. Digital Image Correlation (DIC) The National Institute of Standards and Technology (NIST) performed digital image correlation (DIC) monitoring of the second gusset plate. This system uses two digital cameras in a stereoscopic arrangement. The two cameras take pictures of a randomized pattern applied to the gusset and post-processing software tracks points in the pattern. The system can then provide in- plane strain fields, as well as the full three-dimensional displacement fields of the gusset plate. However, the system is most reliable post-elastic when displacements become large. The data in the elastic regime can be used for qualitative results, but once the plate has yielded extensively, the results become very reliable. Further description of the DIC system can be found in Appendix F. FARO ION Laser Tracker In lieu of conventional LVDTs, a FARO ION laser tracking system was used to measure displacements of discrete points on the specimen. Similar to a total station used for surveying, the system uses a centralized head unit housing the absolute distance measurement (ADM)
39 system, guidance system, and encoders (for zenith and azimuth). It does not have the same distance measurement capacity as a total station (only ~130 feet), but the trade-off is better precision than a total station at about 0.0005 inches. The other difference is the system automatically tracks a spherically mounted reflector (SMR) rather than the user manually adjusting the horizontal and vertical angles to focus on a prism. The primary purpose of these systems is for reverse engineering or quality control purposes, but it provides definite advantages in an experimental environment where one laser measurement is equal to having three LVDTs orthogonally mounted at the same point. The standard SMR is a 1.5 inch diameter steel ball with a prism precisely mounted at the center of the sphere. The SMR can either be touched to a surface of an object or a standard tool set accompanies it that can measure holes, edges, or machine targets. The tracking system automatically follows the motion of the SMR and with a remote control, the user can record the position of the SMR on demand. The system software automatically compensates the measurement accounting for the diameter of the SMR so the measurement correlates to the surface being measured. The software also has the capability of continuous recording such that the SMR can be swept across a surface to attain a true surface profile. The laser tracker had three main uses during the full-scale gusset plate tests. First, it was able to provide accurate initial position/shape of the members and gusset plate before the test began. This data was used to introduce real initial imperfections into the finite element models that predicted specimen behavior. Second, it tracked the motions of targets placed on the specimen (members and gusset) during a test. Finally, post-failure the SMR was swept across the surface of the gussets to determine the final deformed shape. FARO data for each specimen are presented in Appendix H. Strain Gauges Conventional strain gauges were still used to augment the data from the imaging systems. Rosettes and single-axis gauges where applied on the back sides of the gusset plates to provide correlation to the results of the various imaging systems. Strain gauges were also applied at select cross-sections of the five members to determine the axial and bending forces within the members to ensure the loading system is acting as expected. Within the connection region, single-axis gauges were used to help determine how the load is shed from the chords into the gussets, as well as how load is shared between the gussets and the splice plates. Locations of these gauges can be found in Appendix G for each specimen. Data Acquisition All sensor data was collected via a Hewlett-Packard (HP) VXI CT100B mainframe. This included all strain gauges and conditioned voltages from the MTS FlexTest GT controller (i.e., the load and stroke of each jack). The system operated by custom written software that queries
40 the system for data and writes it to a text file and collected data continuously at a rate of 1Hz throughout the duration of testing. The collection software had no capabilities to visualize the data in real time, beyond just showing the current sensor value. To enhance the visualization and post-processing of the data, a detailed Excel spreadsheet was written that queried the data file and performed post-processing to help visualize the raw data easier. The photostress system used its own laptop computer to collect and store images. The data were represented in the form of an image stored in a proprietary format. It had no ability to be synced with an external signal, such as an actuator load signal. Therefore, hand notes were used to identify which strain gauge data should be used for each image collected. The FARO ION system also had its own stand-alone laptop to collect the coordinate data. The data were stored in a proprietary format but the 3-dimensional coordinate data was easily exported to Excel for plotting purposes. This system also did not have the ability to be synced with an external signal and hand written notes were used to sync its data with that from other systems. The DIC system collected camera images via a stand-alone computer system. The system could accept up to four external voltage signals so it could be synced to strain gauge data. In this case, the DIC system collected the conditioned voltages from two actuator loads and strokes so that at any point in time, the images could be synced to the strain gauge data sets via loads being applied to the specimen. Specimen Design The primary intent of the experimental design was to produce physical results of the different failure modes of concern in gusset plate connections and provide data to calibrate finite element modeling techniques. Among these are shear failure of the bolts or rivets, net section fractures in the members, buckling of the plates (either along the free edges or at the end of the compression members), and shear along a plane parallel and perpendicular to the chord. From the preliminary finite element studies it is clear that many of these failure modes interact with one another and that it would be difficult to isolate them in a physical test, particularly as the gussets begin to move out-of-plane. Thus the design of the specimens was broken into two phases, each with six full-scale specimens. The Phase I specimens were intended to assess primarily shear in the A-A plane and buckling at the end of the compression flange. The Phase 2 specimens were meant to investigate the effects of corrosion, stiffening, and other aspects the oversight panel felt appropriate that were not addressed in Phase 1. In Phase 1, four main variables were explored: the type of fastener, the distances within the gusset plate between the ends of the compression diagonal and the other truss members, the length (or slenderness) of the plate edge, and the thickness of the gusset plate.
41 The first test variable considered was the type of fasteners. Two types of fasteners are typical in gusset plates: A502 rivets and A325 structural bolts. For this research, the A490 bolts were chosen in lieu of A325 to make the fastener patterns as small as possible. After considerable research, it was decided for practical reasons that A502 rivets would be very difficult and expensive to install properly. Based on the work of Roeder et al., it was decided to use A307 bolts initially in bearing in lieu of rivets.(20) In addition, further fastener characterization was performed as part of this research described in Appendix C that further validated this claim. Therefore, the unfactored design values for ultimate shear strength for the A307 bolts and the design slip values for the A490 bolts were used to design the fastener patterns for the Phase 1 specimens. The fastener patterns were designed to resist 1200 kips for the chords and diagonals and 440 kips for the vertical member. At times, more fasteners were used than required for strength; this was controlled by other geometric parameters of the overall connection and the fastener patterns were staggered if possible to reduce the amount of overdesign for fastener shear. The standoff distance and free edge length were controlled through the positioning of the compression diagonal and the fastener pattern. The standoff distance is defined as the length of free plate between the compression diagonal and the chord. It is measured via the gap between the lower corner of the compression diagonal and chord which was either 1.0 or 4.5 inches. The 1.0 inch gap was referred to as âshortâ distance and the 4.5 inch gap was called the âlongâ distance. The free edge length was varied by adding additional fastener rows over what was determined via fastener shear design criteria. The standoff distance coupled with the fastener pattern fixed the free edge lengths, which were referred to as the âshortâ free-edge length. However, in two of the specimens, additional rows of fasteners were provided (i.e., over-designed for shear), which increased the free edge length (also referred to as the âlongâ free edge length) without changing the standoff length. The tests are labeled as GPwwwxyz-a, where âwwwâ is the bolt type (either 307 or 490 for the grade of fastener), âxâ refers to the standoff distance (S for short, L for long), âyâ refers to the free edge length (S for short, L for long), âzâ is the plate thickness in eighths of an inch (either 3 or 4 for â inch and ½ inch plate), and âaâ is a sequential number as some of the geometries were replicated. Thus, the test with A307 bolts, â inch plate, long end distance and short edges will be GP307LS3. For brevity this would often be referred to as the 307LS3 or sometimes just the LS3 geometry. Phase 1 The two most compact SS3 geometries are shown in Figure 26. These are considered the baseline specimens where the fastener patterns for the diagonals were as small as possible to transfer the design force of the members as well as using the âshortâ standoff distance. The LS3 geometries shown in Figure 27 maintain the same fastener patterns, but back the compression
42 diagonal out of the connection thus increasing the standoff distance to the âlongâ condition. The free edge length also increases with the LS3 geometries over the baseline SS3 geometries. The philosophy behind the SL3 and SL4 geometries shown in Figure 28 was to maintain the âshortâ standoff distance, but engage more rows of fasteners such that the free edge length is nearly the same as the LS3 geometries. The SL geometry was tested using both â and ½ inch thick plates because each of those thicknesses should result in edge slenderness less than and greater than the existing free edge slenderness criterion in the FHWA Guide. Notice that at times the fastener patterns in the chords and diagonals have fasteners missing from the full pattern. As mentioned before, this was to keep the fastener shear limit-state in balance with the design force as much as possible. At the same time symmetry was maintained about the member force line of action while maintaining a constant pitch and gage around the perimeter of the patterns. For the chord splice, a full pattern of fasteners was used for the first four columns of fasteners in each chord to facilitate bolting of internal web splice plates. There was always a 0.5 inch gap between the two chords at the chord splice. This was done for two reasons: (1) it represented the worst possible situation as most of the reviewed bridge plans called for a âmilled to bearâ condition at compression chord splices and (2) the overall fabrication cost of the two chords was reduced without the ends having to be âmill-to-bear.â To further enhance the strength of the chord splice, additional web, top, and bottom splice plates were added in parallel to the main gusset plate. The schematic shown in Figure 29 shows the placement of these four additional splice plates. The top and bottom splice plates were bolted to the outside of the chord members through the coverplates of the chord cross-section (shown as a green fill in Figure 29). The web splice plates were bolted to the sideplates of the chord cross- section and were inside the chord member (shown with a light blue fill in Figure 29). In all connections, the four splice plates were the same thickness as the gusset plate, and were also cut from the same parent plate as the gusset plate (i.e., the material properties should be uniform for the two gusset and four splice plates.) In all of the Phase 1 specimens, there was a full fastener pattern along the perimeter of the chord members. This was done to balance the likelihood of shear yield on the gross area versus fracture on the net area of the holes in the horizontal plane of the gusset along the top of the chord. Using design yield and tensile properties, the ratio between the shear yield force to the shear fracture force for all six Phase 1 specimens was 0.98 with a full fastener pattern and 1.16 with a staggered fastener pattern. In the Phase 1 testing, there was a hydraulic malfunction that accidently crushed the GP490LS3 geometry before it had failed under controlled conditions. Therefore, in the purchase of some Phase 2 gusset plates, replacement 490LS3 plates were attained and it was called GP490LS3-1.
43 59.0 0.5 17.6 26 .4 27 .9 14 .8 13.4 54.8 0.5 16.0 24 .9 26 .5 13.41 3. 3 Figure 26. Dimensions in inches for SS3 specimens. (left) GP307SS3. (right) GP490SS3. 66.5 0.5 22.5 31 .4 29 .5 19 .9 18.0 19.4 59.0 0.5 28 .0 26 .2 18.016 .5 Figure 27. Dimensions in inches for LS3 specimens. (left) GP307LS3. (right) GP490LS3. 22.6 66.5 0.5 31 .5 29 .4 13.1 19 .9 Figure 28. Dimensions in inches for SL3 and SL4 specimens.
44 Figure 29. General detailing of chord splice plates. End view (left). Elevation view (right) Phase 2 The Phase 2 specimens did not introduce any new connection geometries over the five used in Phase 1. Rather, Phase 2 investigated variations of some Phase 1 geometries that investigated the effects of corrosion, retrofit strategies with shingle plates and stiffening angles, and for one connection a defined shear resistance failure. The Phase 2 specimens were selected at three distinct points in time after the Phase 1 testing began, primarily to react to outcomes during Phase 1 and from panel input through quarterly progress reports. Unlike the Phase 1 specimen, all Phase 2 specimens were tested with the addition of a work point brace that provided out-of-plane restraint to the work point. This is described in Appendix B. Specimens with Simulated Corrosion Early in Phase 1 it was noted that specimens replicating corrosion would have to be tested as part of the overall research program and it was decided to limit this to just corrosion within the gusset plates, not the fasteners. There were many questions as how to integrate non-uniform remaining sections into load rating calculations and how the section loss would affect various limit-states. To make the corrosion as realistic as possible the intent was to corrode the gusset plate specimens by cathodic means. The obstacle to this approach is it would be a timely process which was calculated to take approximately 6 months. Therefore, when the Phase 1 gusset plates were purchased, so were two additional 307SS3 geometries that could be cathodically corroded while the Phase 1 testing was occurring. Unfortunately, the cathodic corrosion approach did not work and in the end the corrosion was simulated by milling away sections from the plate in a predetermined pattern. Shown in Figure 30 is the shape of the simulated corrosion pattern for each of these two connections. These two specimens were named GP307SS3-1 and GP307SS3-2. As can be seen,
45 the simulated corrosion shape was the same for all four plates and was symmetric for each connection. What cannot be pictorially shown in the figure is the pattern that was milled into the surface of the plate that would be interior to the connection. The shape was derived from looking at pictures of corroded gusset plates in inspection reports submitted to the research team by the state of Illinois and the city of Chicago. What was evident in those reports was that corrosion was often non-uniform and in many cases vast areas of the plate between members suffered from section loss. The depth of the corrosion was purposely different for the tension and compression diagonal side of the plate in order to assess non-uniform corrosion across a plate. Each of the plates were 0.375 inches thick and the figure outlines a percentage of the plate thickness that was removed by milling. The only difference between the two separate connections was that the 50% and 30% thickness reduction was flip-flopped for each connection. The panel had concerns that the simulated corrosion patterns in 307SS3-1 and 307SS3-2 did not cover enough situations, and asked that two additional Phase 2 specimens investigate other corrosion patterns. Primarily some panel members preferred to see the simulated corrosion only on one plate (so the connection stiffness would be unbalanced) and that the shape should be more narrow-banded above the chord. Like the other simulated corrosion specimens, these two additional specimens also used the Phase 1 307SS3 geometry. In each case, only the plate on the north side of the connection had simulated corrosion milled into it; the south plate was undamaged. The third and fourth simulated corrosion specimens were called GP307SS3-3 and GP307SS3-4 respectively. Each of these specimens used the same corrosion pattern on just their north plate as shown in Figure 31. The simulated corrosion pattern is 1.5 inches tall and 48 inches long, and was milled 0.188 inches deep into the plate for a nominal 50% section loss. The bottom of the simulated corrosion pattern was in-line with the top edge of the chord side plate where corrosion would develop if this were a real lower chord truss connection. The intent of the GP307SS3-3 specimen was to investigate the role of corrosion on just one plate of the connection. The GP307SS3-4 connection then investigated how to retrofit this simulated corrosion pattern through the use of a shingle plate added to the exterior of the connection. The schematic shown in Figure 32 shows the corrosion pattern on the inside of the plate, but also the outline of the shingle plate that was also bolted to the outside of the plate. Again, the south gusset plate did not have simulated corrosion, nor a shingle plate. The shingle plate was installed with the primary gusset plate and therefore did not represent the stress conditions that would be present in a gusset plate if the shingle were to be added as a retrofit. This was deemed too unsafe to perform in the lab while under hydraulic control.
46 50% 30% 30% 50% 30% 50% 50% 30% GP307SS3-1 North GP307SS3-1 South GP307SS3-2 North GP307SS3-2 South 48.0 12 .0 Figure 30. Pattern of corrosion milled into interior surface of 307SS3-1 plates (top) and 307SS3- 2 plates (bottom). GP307SS3-3 North 48.0 1. 5 50% Figure 31. Corrosion pattern of GP307SS3-3 and GP307SS3-4 north plate.
47 GP307SS3-4 North 48.0 1. 5 50% Figure 32. Corrosion pattern of GP307SS3-4 north plate. GP490SS3-1 and GP490LS3-2 An interim meeting with the panel was held after the fourth Phase 1 specimen was tested to give the panel an opportunity to personally see the experimental testing. At that point the first four Phase 1 specimens had failed via buckling and it appeared a shear failure would not occur throughout the experimental testing. In that meeting, the panel requested a retest of one Phase 1 geometry; however, they requested that the researchers fully restrain it out-of-plane to force the shear failure. In addition to the work point brace already being used in Phase 2, this specimen also braced the compression diagonal against the shearwalls so it could not move out-of-plane. The research team opted to retest the 490SS3 geometry as it was the most compact plate that would have the greatest success of shearing within the load capacity of the frame and it was called GP490SS3-1. A schematic of the plate geometry can be seen in Figure 33. The only difference made with this geometry was 12 bolts were removed from the chord fastener pattern. This increased the net section area so as to have a greater success of causing a gross shear yield failure. At the same meeting, the panel also requested testing an edge stiffened connection. The research team opted to retest the 490LS3 geometry as it had the lowest buckling resistance and thus would benefit the most if it could be stiffened. The intent of this specimen was to investigate the edge stiffening as a retrofit to enhance buckling resistance, not to assess the role of free edge slenderness criteria. Prior to finalization of the tested geometry, preliminary finite element analysis was performed to understand how much strength increase the retrofit could provide. Three scenarios were investigated: placing stiffening angles on the interior free edges around the compression diagonal, adding a plate diaphragm between the same interior angles, and placing the angles external to the connection. These three options are shown in Figure 34. These three retrofit strategies were analyzed with two different Phase 1 specimen geometries, the 490SS3 and 490LS3. Even though this Phase 2 specimen was to use the 490LS3 geometry, analyzing with two different geometries was done for analysis redundancy. The results of the analysis are
48 shown in Table 3 and presented in terms of the maximum load proportioning factor (LPF). The LPF is a multiple of the reference load state by which the analysis can no longer converge to a solution and is really a non-dimensional form of peak load at failure. Typically, a state of non- convergence was due to nonlinear geometric effects, in this case buckling. The table presents a percentage increase in LPF for each of the three retrofits over the connection with no stiffening. For each of the two connections, the interior angles were inadequate to increase the buckling resistance of the connection, at best only able to provide 3% extra strength. Adding a diaphragm plate between angles increased the buckling strength by 11.5% and 30.1%; however, the drawback with this retrofit is it reduces the ability to inspect inside the connection. Therefore, the best retrofit was to externally stiffen the entire plate edges on each side of the compression diagonal which had even more strength than the internal angles with a plate diaphragm (25.3% and 44.9% increase of the unstiffened case). The disparity of the three retrofit strategies arises because in all situations, when gusset plates buckle, they always buckle in a sidesway mode. In this case, interior angles do not contribute much stiffness against this mode. The key was to add stiffness across the planes that would bend in sidesway; therefore, for the external angle retrofit to be most effective, it must be carried into the chord and vertical fastener patterns. Shown in Figure 35 is the final geometry of the GP490LS3-2 specimen. The edges were stiffened with 3x3x½ inch angles that were bolted to the outside of the gusset plates. Finally, in accordance with the pretest analysis results, the stiffening angle was placed along the entire length of the gusset plate edge, thus bridging across the planes that would bend in sidesway. Figure 33. Dimensions in inches of GP490SS3-1.
49 Figure 34. Angle stiffening options. Internal angle (top). Internal angles with plate diaphragm (middle). Exterior angles (bottom).
50 Table 3 Results of Preliminary Edge Stiffening Strategies GP490SS3 GP490LS3 Max. LPF % Increase Max. LPF % Increase No Stiffeners 0.712 - 0.579 - Interior Angles 0.715 0.4 0.598 3.3 Interior Angles with Plate Diaphragm 0.794 11.5 0.753 30.1 Exterior Angles 0.892 25.3 0.839 44.9 Stiffening angles were L3x3x½ inch and plate diaphragm was the same thickness as the gusset plate âLPFâ stands for Load Proportioning Factor Figure 35. Dimensions in inches of GP490LS3-2. Stiffening angles shown in red.
51 Applied Loads During Testing Before each connection was tested to failure a series of elastic tests were performed primarily to understand how load flowed through the gusset plates, primarily based on data from the photostress system. In these tests, the loads were proportioned until the maximum stress in the plate was about 70% of nominal yield according to a finite element simulation. Table 4 outlines the variety of normalized load combinations used for the elastic loading scenarios. For all but one specimen, 307LS3, only load combinations 1-11 and 13-15 were used. Specimen 307LS3 was tested with both chords in tension and load combinations 12a-12h were used exclusively for that specimen. The elastic load scenarios were repeated with and without horizontal continuity plates in the chords. After the two elastic tests series (with and without continuity plates) were complete, a load combination was selected and the connection was proportionally loaded until failure. Generally, to loading was stepwise, monotonic, with between 10 and 20 load steps until the specimen failed. At load holds, FARO and DIC data were collected, while strain data was continuously monitored through the loading. The load combination used in the failure test is shown in Table 5 for each of the 13 specimens.
52 Table 4 Reference Load Combinations Load Combination F1 F2 F3 F4 F5 Shear on A-A plane 1 -1 0.707 0 -0.707 0 1 2 0 0.707 0 -0.707 1 1 3 -0.707 1 0 -1 0.707 1.414 4 -0.5 1 -0.207 -0.707 0.707 1.207 5 -0.5 0.707 0.207 -1 0.707 1.207 6 -0.707 1 -0.207 -0.707 0.5 1.207 7 -0.707 0.707 0.207 -1 0.5 1.207 8 -1 0.707 0.207 -1 0 1 9 -0.207 0.707 0.207 -1 1 1.207 10 -1 1 -0.207 -0.707 0.207 1.207 11 -0.207 1 -0.207 -0.707 1 1.207 12a -1 0.330 0.117 -0.496 -0.416 0.584 12b -1 0.650 0 -0.650 -0.081 0.919 12c -1 0.375 0 -0.375 -0.469 0.531 12d -1 0.088 0 -0.088 -0.876 0.124 12e -1 0.672 -0.119 -0.504 -0.168 0.832 12f -1 0.504 0.119 -0.672 -0.168 0.832 12g -1 0.697 -0.246 -0.348 -0.261 0.739 12h -1 0.348 0.246 -0.697 -0.261 0.739 13 0.431 0.322 0.117 -0.483 1 0.569 14 -0.597 1 -0.090 -0.874 0.728 1.325 15 -0.446 0.482 0.365 -1 0.602 1.048 15m -0.531 0.600 0.282 -1 0.600 1.131 16 -0.531 1 -0.282 -0.600 0.600 1.131 Sign convention of above load ratios F1 F2 F3 F4 F5 East ChordWest Chord Te ns ion D iag on alVe rti ca l Compression Diagonal
53 Table 5 Failure Load Combination for Each Specimen Phase Specimen Load Combination 1 307SS3 4 490SS3 3 307LS3 12g 490LS3 15m 307SL3 3 307SL4 3 2 490LS3-1 15m 490LS3-2 16 490SS3-1 15m 307SS3-1 4 307SS3-2 5 307SS3-3 5 307SS3-4 5 ANALYTICAL Finite element studies were run from the beginning of the project all the way through completion. Within that time period, there was an evolution of how the modeling was conducted, along with the focus of its outcome. At first, the NCHRP panel requested immediate in-depth analysis of four representative joints taken from real bridges; this was described in Chapter 1. While it did not lead to revision of the FHWA Guide, the task did highlight issues that were unknown to the research team such as the role of chord splice plates, and the intricacies associated with multi-layered gusset plates. In this phase a finite element modeling philosophy for gusset plates was first established, loading the connections in a two-panel truss system, and representing the joint with nonlinear shell elements connected with fastener elements representing the bolts or rivets. The second phase of the finite element modeling effort refined the initial modeling philosophy by benchmarking against the experimental specimen results. The first five tested connections were modeled pre- and post-test to establish what had to be done to produce accurate results. In this stage, the fastener elements were refined based on single shear lap splice tests conducted as part of the experimental program (described in Appendix C). It was also found that the initial shape of the gusset plates was very important for attaining highly correlated results between the model and the experiment. All 13 of the experimental specimens were modeled pre-test to attain predictions of the behavior, necessary for setting up the data collection and hydraulic interface computers.
54 The final, and largest, part of the finite element modeling effort was conducted in parallel with the testing of the Phase 2 experimental specimens. This was the parametric study that analyzed a wide variety of gusset plate geometries and evaluated their failure modes. The data from the parametric finite element study and the results from the experimental testing were used in the calibration of resistance equations. The remainder of this section will describe the specific details of how the simulations were performed. Modeling Philosophy In this research, finite element simulations were performed using Abaqus.(18) In all models, gusset plates, splice plates, and parts of members that are in the vicinity of the given gusset plate joint are modeled using four-node, reduced integration, linear formulation shell elements referred to as S4R elements within Abaqus. It was targeted to model truss members using shell elements within a minimum of three times the connection length of a given truss member (i.e., the shell representation of the member extended two connection lengths beyond the edge of the gusset). However, to increase efficiency of the finite element modeling procedures, members are modeled with shell elements for the first 200 inches unless otherwise noted. A typical connection model is shown in Figure 36. All the parts not shown as lines were modeled using S4R elements. The remaining lengths of the truss members outside of the 200 inch limit, as well as the truss members that are not connected to the gusset plate joints, were modeled using 2-node linear beam elements (the B31 element in Abaqus). Multi-point constraints were used to connect a cross-section modeled with shell elements to an end node of a beam element. The basic concept of the model was to isolate the connection of interest into a two-panel truss system. In all subsequent discussions, points in two-panel systems are always referred to as U1 through U3 for points on the upper chords and L1 through L3 for points on the lower chords. For all cases, the gusset plate joints under consideration are located either at U2 or at L2 locations. For example, for the connection shown in Figure 36, the gusset plate joint is located at U2. Also represented in this figure are the boundary conditions imposed upon the model. All the end nodes of truss members that are on the outside perimeter of the two-panel system are restrained in the out-of-plane direction. For in-plane movements, a simply supported condition is modeled. In addition, an out-of-plane restraint is applied at one node at the center of the top or bottom splice plates, to represent the out-of-plane restraint typically provided by floor systems. However, the out-of-plane reaction due to floor system restraint was found to be negligible in all the study joints. As shown in Figure 36, all the loads representing dead and live loads are applied in the plane of the truss to nodes that do not have restraint in the direction of the load. The only exception was that of the vertical member. For vertical members, the panel point load was applied at the intersection of the beam and shell element transition. This decision was based on the fact that in most bridges, this load is transferred from a floor beam which is attached below the joint. By applying this load at the end node of a beam element, the issues associated with the stress concentrations at the location where the load is applied to the shell element can be avoided.
55 In the analysis of the experimental specimens, the joints were modeled as they were tested, and did not require the two-panel truss to apply the loads. Rather, loads and boundary conditions were modeled as they were applied in the laboratory. The meshing of the gusset plates and members used the same philosophy as those in the two-panel truss configurations. Geometric Imperfections For all connection models, excluding the laboratory specimens, Figure 37 shows typical geometric imperfection shapes used in the simulations. It can be seen that geometric imperfections are incorporated not only on the gusset plates but also on the compression member itself. These imperfections are generated by a separate linear elastic analysis of the given test joint model. In this separate analysis, pressure loads are applied on the gusset plates so that out- of-straightness of gusset plates on the compression diagonal side is generated and out-of-plane displacements are applied at the end of the compression diagonal so that initial out-of-plane plumbness of the member is also generated. These imperfections generally look like the first mode buckling behavior of the gusset plate which is an out-of-plane sway mode. While real imperfections may not follow this shape, in a buckling analysis it would represent the lower bound of the buckling resistance produced by the analysis. After the deformed shape is obtained from the pressure load analysis, the deformations are scaled such that the maximum magnitude of the out-of-straightness of gusset plates and the out-of- plumbness of a diagonal member match selected maximum imperfection limits. The selected limits are: (1) Lmax/150 for the maximum out-of-straightness of gusset plates, where Lmax is the maximum length of free edges adjacent to the compression diagonal and (2) 0.1Lgap for the maximum out-of- plumbness of the compression diagonal, where Lgap is the smallest length of the gap between the compression diagonal and the adjacent members. For the connection shown in Figure 37, the vertical free edge between the left chord and the compression diagonal gives Lmax of 35.17 inches. Therefore, the maximum out-of-straightness of the gusset plate was scaled to be 0.235 inches. In addition, Lgap is 1.0 inch between the compression diagonal and the vertical member. Therefore, a maximum out-of-plumbness of the compression diagonal of 0.1 inch was used. While the limits may seem arbitrary, the research team tried to use relevant codes and standards to determine what kind of fabrication or erection standards may be applicable to truss connections that may influence the alignment of truss members and hence cause gusset plate imperfections. However, no specific language could be identified that spoke to allowable tolerances of as-built gusset plates as most tolerances have to do with allowable sweep of compression members. For instance, the American Welding Society D1.5 âBridge Welding Codeâ contains a section on dimensional tolerances which limits the out-of-straightness of welded members (i.e., built-up truss members) to 0.125 inches per 10 feet of length which translates to L/960 or an end slope of 0.00419 (based on circular curvature).(19) If the gusset plate is assumed to be drawn to the framed member by bolting it will assume the same slope as the member since it is much more flexible out-of-plane. Thus a 48 inch wide plate could be pulled
56 out-of-straight by 0.20 inches at maximum tolerance. Again, since this is not exclusively meant for gusset plates, a sensitivity study on the magnitude of the imperfections was performed early in the project. What was found is once the imperfections exceeded approximately 0.06 inches, the change in the buckling resistance was relatively small. Therefore, imperfection limits used in the research were a middle ground between what could be found in a relevant specification versus pure analysis. In the analysis of the experimental specimens, the real shape of the gusset plates and orientation of the members extracted from the FARO data was entered directly into the analysis and an assumed shape was not used. Material Properties Figure 16 shows the true stress-strain curves for Grade 50 and Grade 100 steel used in the parametric study simulations. The yield strength of the material was determined based on a bias of 1.10 of true yield strength from the nominal specified and a reduction of 2 ksi to account for the difference between the 0.2 % offset and static yield strengths. The 2 ksi reduction was based on observations collecting coupon data in support of the experimental testing. Therefore, for Grade 50 steel, the static yield strength, Fys, is 50 ksi à 1.10 â 2 ksi = 53 ksi. After this decision had been made, it was found that static yield strength typically has a bias of 1.05, or 52.5 ksi for a Grade 50 material which reinforced the chosen value.(21) The true stress-strain curve shown in Figure 38 is based on curve-fitting data from some of the coupon tests performed as part of the experimental program. The curve-fit defined the shape of the curve post-yield and it was adjusted to have a yield strength of 53 ksi. In the simulations, all the data points shown in Figure 38 are input explicitly from the point where the plastic strain is 0.0 to 0.2. Abaqus assumes a flat plateau after the last data point. As mentioned above, the Grade 100 steel was also used in the simulations of selected cases. The static yield strength of Grade 100 steel is also obtained as described above and as a result, Fys = 100 ksi à 1.10 â 2 ksi = 108 ksi. The true stress-strain curve shown in Figure 38 is based on curve-fitting data of coupon tests performed for the experimental member plate which was ASTM A514. The stress-strain curve data of Grade 100 steel for test simulations is input in Abaqus as described above. When modeling the experimental specimens, the real plate properties were used. As described further in Appendix D, 14 coupons were tested from each parent plate that the gusset and splice plate for each specimen were fabricated from. A single material model was then defined for each specimen by averaging the results from all 14 coupons. Fastener Strengths For all the test simulations, the fasteners are modeled with nonlinear strength properties. In Abaqus, fasteners can be modeled using connector elements with nonlinear properties. Figure 39
57 shows the nonlinear shear-force and shear-displacement curves for A307 and A490 bolts and hot-driven rivets. There are stark contrasts between the three models because they are in terms of the shear force, not stress. For instance, there is a marked difference in cross-sectional areas between the 7/8 inch diameter A307-N bolt and nominal 7/8 inch rivet driven into a standard oversized hole. In addition, these fastener models also considered the deformation of the bolt holes as holes were not considered in the finite element simulation. For this reason, the curve for a 7/8 inch A490-X bolt did not result in the shear failure of the bolt, rather all the deformation was ovalization of the bolt hole leading to the apparent ductility of the fastener model. The fastener properties are modeled such that the strength curves are applied to the square root of the sum of squares of all the shear loads within the fastener element. For the places where fasteners connect three or more plates, these fasteners have two or more layers of connector elements. For the out-of-plane component, elastic behavior is assumed with a stiffness of EA/L, where E is Youngâs modulus, A is the cross-section area of a fastener, and L is the total length of a fastener. Relative movements at the ends of connector elements are modeled such that relative rotations are restrained but the independent displacements are allowed. Failure Criteria Determining the point of failure for each analytical model was controlled by three criteria; the first one reached determined the failure point. These were: 1) Peak of the load versus displacement curve In general, the load versus displacement curve from the analysis has a loading and a post- peak unloading path. 2) 4% equivalent plastic strain (PEEQ) at mid-thickness In the finite element models, the actual bolt holes are not modeled and fracture of the steel is not incorporated into the nonlinear material model. Hence, the models cannot capture net section limit-states. This value is arbitrarily set at 4%, but the experience of the research team has found this to be an indicative strain level where faith in the model may begin to become unreliable (i.e., when net section failures may occur considering net sections are not modeled. 3) 0.2 inch fastener shear displacement In the component tests performed and reported upon in Appendix C, it was noted that generally rivets and bolts failed in shear after approximately 0.2 inches of shear displacement. Since the fastener models used in the analyses are also nonlinear, this limit represents when fasteners may begin to fail and control the strength of the connection. Overall, this limit is rarely controlled. .
58 Figure 36. Typical loading and boundary conditions. Figure 37. Typical geometric imperfection shapes on gusset plate joints.
59 Figure 38. True stress-strain curves for Grade 50 and Grade 100 steel. Figure 39. Nonlinear shear-force shear-displacement curves 7/8 inch A307, A490 bolts and hot- driven rivets. 0 20 40 60 80 100 120 140 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Tr ue S tr es s (k si ) Plastic Strain (in/in) Grade 50 steel (Fy=53 ksi) Grade 100 steel (Fy=108 ksi) 0 10 20 30 40 50 60 70 80 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 Fa st en er F or ce in S in gl e S he ar (k ip ) Displacement (inch) 7/8 inch A307-N bolt 7/8 inch A490-X bolt 7/8 inch hot-driven rivet
60 Analysis Matrix In total there were 201 different models analyzed as part of the parametric finite element study. This section will briefly describe the matrix, but more detailed information can be found in Appendix I. Three main truss bridge configurations were used in the parametric study. These are (1) Warren trusses with vertical members, (2) Pratt trusses, and (3) Warren trusses without vertical members. Examination of the available bridge plans indicated that longer bridges with continuous spans generally have Warren configurations with or without vertical members (see Appendix A). In addition, the NCHRP 12-84 project panel indicated that Warren trusses without verticals are common in more recent construction, and that Pratt truss configurations are used mostly for shorter single span bridges. For the selected parametric bridge configurations, a number of typical joints were extracted and designed for different locations within the hypothetical bridge spans. The selection of locations and the corresponding loading scenarios for these joints are discussed below. In addition to the test joints for the above three bridge configurations (Warren with verticals, Pratt, and Warren without verticals) six additional test joints were designed to incorporate other specific cases. These include corner joints, joints that have a positive angle between the chord members on each side of the joint, and joints that have a negative angle between the chord members on each side of the joint. With the exception of corner joints, all the test configurations are two-panel subassemblies with the test joint in the middle. By using two-panel systems, the loads from the bridge can be applied at the ends of the subassembly and the two-panel system in essence imposes realistic equilibrium and kinematic conditions at the test joint. Figures 40 through 43 summarize the 20 base geometries investigated in the parametric study. Within the four figures, the joints are titled based on location within a truss either being at midspan, near a pier, at a pier, and inflection point. The location within the truss gives a broad description of the type of loading imposed upon the gusset plate. For instance, midspan joints have light loading on the diagonals, but very large chord loads. Joints at a pier generally have very large loads where all members are either compressive or tensile depending if it is an upper or lower joint. Joints at an inflection point generally have high diagonal member loads with chord loads in a coincident direction leading to large shear forces through the gusset. In addition, different truss depths were used to attain different framing angles between diagonals and chords. The 20 base geometries were designed to meet the five resistance checks of the FHWA Guide. The members had their ends chamfered to create the most compact joints possible. The 20 connections were first analyzed according to the FHWA Guide design then additional variations on these 20 base geometries were developed to construct the matrix of 201 models. These additional model parameters are described herein.
61 Plate Thickness The advantage to using shell element formulations in a parametric study is that the plate thickness can easily be changed to create a new model. Many of the base geometries were quickly reanalyzed by varying the gusset plate thickness from 0.25 to 0.625 inches in 0.125 inch increments. In doing this, there was a pronounced transition from buckling to shear failures as the plate thickness increased. Mill-to-Bear versus Non-Mill-to-Bear Compression Splices Four connections were selected to study the effects of mill-to-bear conditions at compression chord splices. Since the original series of study joints had a gap between adjoining chord members, the joint failed via crushing of the gusset in the chord splice. Adding the mill-to-bear condition in select joints allows for the next failure mode to be identified. The selected connections are P1, P11, P19, and P20. In finite element models, the continuity between chord members is modeled by tie constraints between all the nodes of the cross-section at the end of chord members. That is, all the displacements and rotations of the cross-section at the end of one of the chord members are completely tied to the cross-section of the other chord member; these are kinematic couplings that actually reduce the overall degrees of freedom of the model. Material Strength All the initial joints were analyzed using Grade 50 materials for their gusset plates and splice plates. To study the effect of high-strength materials on the behavior of gusset plate connections, three test joints were selected to be analyzed using Grade 100 materials for gusset and splice plates. For the first set of analyses, the gusset plates have the same thickness as the initial designs but have Grade 100 material. Then for the second set of analyses, the gusset plate thicknesses are reduced so that the plates have the same strength based on their area and the material strengths. Member Chamfer versus No Member Chamfer As mentioned above, the initial set of joints was designed using chamfered members. In other words, all these joints have diagonals that are chamfered as much as possible until only two fasteners can be attached at the end of members. When members are chamfered, the areas between chamfered edges and the adjacent members are extremely small and as a result, the gusset plate area is relatively small. After the initial set of joints was analyzed, a number of test joints were selected and redesigned with unchamfered members. In general, when the members are unchamfered, the areas between diagonals and chords and/or diagonals and vertical members are larger than the ones in joints with chamfered members. As a result, the lengths of free edges are longer (relative to the overall area of the plate). Therefore, by varying member chamfers, the effect of larger distances between members and longer free edges on the failure modes and maximum capacities was studied.
62 Shingle Plates All the gusset plate joints were initially designed without shingle plates. However, joints at piers generally have shingle plates because otherwise the main gusset plates need to be significantly thicker in order to transfer large member forces into the pier. Therefore, several cases were selected to study the behavior of shingle plates. The goal of this study was to develop design methods for shingle plates, which can be one retrofit option. Edge Stiffening One of the common practices to retrofit gusset plate joints is to add edge stiffeners on the free edges. Engineers commonly add short angles on the inside of gusset plates between members, e.g., between a chord and a diagonal. In this study, the effect of stiffeners on the maximum capacities of gusset plate joints was studied. Corrosion The effect of corrosion on the behavior of gusset plate joints was also studied in this research. A number of joints were selected to be modeled including holes and corroded regions. These corroded test cases were then analyzed with shingle plates to investigate the benefits from adding shingle plates as a retrofit method for corroded gusset plate joints.
63 Figure 40. Warren with vertical configurations. Case P1, Joint at midspan Case P2, Joint at midspan Case P3, Joint at pier Case P4, Joint at pier 30003000 30003000 2500 2500500 5500 30 ft 55 ft 55 ft 60 ft 300 500 200 3000 3000 2900 2900 424 28 3 40 ft 40 ft 300 500 200 3000 3000 2900 2900 -42 4 -283 40 ft 40 ft Case P5, Joint near pier Case P6, Joint near pier Case P7, Joint at inflection point Case P8, Joint at inflection point 15003000 1500 3000 2500 500 2000 30 ft 60 ft 30 ft 1200 4800 4800 1000 1000 2400 1900500 40 ft 40 ft 20 ft -22 60 2470 1600 500 2460-358 0 1100 3200 3200 2200 2200 40 ft 20 ft 40 ft 500 27.5 ft 40 ft 1100 1600 1600 16001600 1600 -2100 21 00 40 ft40 ft 30003000 30003000 2500 25005000 30Â ft 60Â ft
64 Figure 41. Pratt configurations. Figure 42. Warren without vertical configurations. Case P9, Joint near pier Case P10, Joint near pier 360 30 ft 360 260 110 730 730 150 368 156 30 ft 30 ft T T 360 30 ft 360 260 110 730 730 150 36 8 15 6 30 ft 30 ft Case P11, Joint at midspan Case P12, Joint at pier Case P13, Joint near pier Case P14, Joint at inflection point 3000 40 ft 35 ft 3000 3000 3000 250 250 500 3000 60 ft 30 ft 50002500 2500 3000 3000 3000 1650 2500 500 30 ft 30 ft 30 ft 3000 3000 1280 1280 45 ft 60 ft 350 750 1600 500 40 ft 40 ft 40 ft 40 ft 1350 1350 1350 1350 27.5 ft 350
65 Figure 43. Other configurations.
