Paper Title: STUDY OF FATIGUE-INDUCED CRACKS IN THE CONNECTION 1 PLATES OF SKEWED HIGHWAY BRIDGES 2

3 4 5 Authors: Gengwen Zhao 6

Graduate Research Assistant 7 The Bridge Engineering Software and Technology (BEST) Center, 8 Dept. of Civil and Environmental Engineering 9 University of Maryland, College Park, MD 20742 10 Tel: 404-317-1522 Email: gwzhao@umd.edu 11

12 Chung C. Fu, Ph.D., P.E. 13 Director/Research Professor 14 The Bridge Engineering Software and Technology (BEST) Center, 15 Dept. of Civil and Environmental Engineering 16 University of Maryland, College Park, MD 20742 17 Tel: 301-405-2011 Email: ccfu@umd.edu 18

19 Tim Saad 20 Graduate Research Assistant 21 The Bridge Engineering Software and Technology (BEST) Center, 22 Dept. of Civil and Environmental Engineering 23 University of Maryland, College Park, MD 20742 24 Tel: 301-405-2011 Email: tsaad@umd.edu 25

26 Call Title: 27

Special Topics in Steel Bridges 28 29

Sponsoring Committee: 30 AFF20 - Steel Bridges 31 32

Length: Text 4,179 words 33 Tables (3) 750 words 34 Figures (9) 2,250 words 35 ------------------------------------------ 36 Total 7,179 words 37 38 39

Zhao, Fu, Saad 2

ABSTRACT 1

Fatigue-induced cracking is a failure mode that may be experienced by some steel bridges after 2 reaching their original design life, in particular bridge structures that have experienced increasing 3 traffic volume and weight, deteriorating components, as well as a large number of stress cycles. 4 This paper presents a case study of fatigue assessment of a steel interstate highway bridge through 5 real time monitoring under traffic. The bridge is a skewed single-span composite steel I-girder 6 structure with K-type cross-frame utilizing bent-plate connections. The study also included 7 numerical analysis using 3D global finite element models. Based on the simulated traffic flow, 8 statistical dynamic responses such as displacements and stress-ranges were studied for the cause of 9 fatigue cracks that occurred in some cross-frame connections. Meanwhile, long-term field 10 monitoring was also conducted. Furthermore, the influence of connection plate configuration and 11 bracing system configuration was studied using a series of controlled finite element tests. Based on 12 the information from the field tests, simulated numerical analytical results were verified. Thus, the 13 performance of highway bridges under truck load can be predicted in a more realistic way to 14 estimate the fatigue performance of highway bridges. 15

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Keywords: Fatigue, Finite Element Modeling, Traffic Loading, Cross-Frame 17

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Zhao, Fu, Saad 3

INTRODUCATION 1

Bracing in steel bridges serves multiple purposes. Bracing members provide an overall stability to 2 the girders as well as directly increase the stiffness and strength of the system in resisting lateral 3 and/or torsional loads. Additionally, cross-frames may also help distributing gravity loads in the 4 structure [1]. Many different configurations of cross-frames or diaphragms have been employed in 5 the construction of steel plate-girder bridges [2]. 6

Generally speaking, the most common bracing of I-girder bridge systems is a discrete 7 torsional system consisting of cross-frames with a K- or X-configuration. Solid plate or channel 8 diaphragms are also used. The braces are usually fabricated from angles or of solid diaphragms 9 constructed with channel-type sections for ease in attachment to girder stiffeners [1, 2]. In addition, 10 top or bottom lateral truss bracing may be needed to resist lateral loads and provide additional 11 stability. For bridges with skewed supports, there are three bracing layouts commonly used [3]: 12

1. Bracing is placed parallel to the skew angle; 13

2. Bracing is placed perpendicular to the girder line in a staggered layout; 14

3. Bracing is placed perpendicular to the girder line in an unstaggered layout. 15

However, one problematic area with cross-frames placed parallel to the skew angle can be 16 the connection details that are used between the brace and the girders. Fabricators may use a bent 17 plate to make the connection between the brace and the connection plate (web stiffener) [1]. The 18 current practice of fabricators is: 19

1. Weld bearing stiffener normal to girder; 20

2. Install/weld connection stiffener normal to girder, next to the bearing stiffener; 21

3. Weld bent gusset plates to cross-frames; 22

4. Bolt bent gusset plates to the connection stiffener. 23

Such a detail allows the fabricator to utilize a connection plate that is perpendicular to the 24 web plate; however the bent plate connection can reduce the effectiveness of the brace [4]. One 25 solution to eliminat the bent plate is to orient the connection plate parallel to the skew angle; 26 however, such a detail can be complicated for larger skew angles. In addition, fatigue tests on the 27 angled stiffeners showed a much lower life compared to perpendicular stiffeners [4]. 28

This paper aims to discuss fatigue cracks caused by bent plates. The study focuses on 29 conducting loading time-history analyses of highway bridges under simulated truck loading. An 30 instrumented skewed single span composite steel I-girder bridge with inverted K-type bracing 31 system is numerically studied. The simulated responses of the bridge are examined. Later, 32 preliminary field tests and long-term monitoring of the studied bridge were also introduced. Based 33 on the information from field measurements, simulated numerical results were validated. Thus, the 34 performance of highway bridges under truck load can be predicted in a more realistic way to 35 estimate the fatigue performance of highway bridges. Based on the findings, engineers need to 36 recognize the importance of bracing systems and connection details in facilitating construction and 37 improving the overall service life of the bridge. . 38

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FATIGUE CRACKS AND BRIDGE TESTING 40

Zhao, Fu, Saad 4

Bridge Introduction 1

MD Bridge No.15042 is a simple-span composite steel I-girder bridge with a span length of 2 140’-0”, located at I-270 over Middlebrook Road near Germantown, Maryland. This bridge is 3 comprised of two structures for the northbound (NB) and southbound (SB) roadways respectively, 4 separated at the centerline. It carries three traffic lanes in the south and four traffic lanes in the 5 north with equal lane widths of 12’-0”. 6

The southbound superstructure provides a curb-to-curb roadway width of 61’-2” and 7 consists of eight identical welded steel plate girders with a composite reinforced concrete deck 8 constructed with shear connectors. The eight girders are equally spaced at 7’-11” and each girder 9 has a constant web depth of 60” throughout the entire bridge. The northbound superstructure 10 provides a curb-to-curb roadway width of 73’-1” and consists of nine identical welded steel plate 11 girders with a composite reinforced concrete deck constructed with shear connector. The nine 12 girders are equally spaced at 8’-5” and each girder has a constant web depth of 60” throughout the 13 entire bridge. This bridge has a 76 degree parallel skew of its bearing lines (or 14 degree measured 14 from normal). The cross-frames are inverted K-type braces with bottom chords only. All of them 15 are parallel to the bearing lines. Girders of the southbound superstructure are numbered as G1 16 through G8 from the exterior to the centerline of the bridge. The cross section is depicted in Figure 17 1. 18

Designed in 1988, the I-270 Bridge over Middlebrook Road has been in-service for over 20 19 years. In addition to deterioration caused by environmental factors, the bridge structure has also 20 been subjected to increasing traffic volume and weight. Four fatigue cracks as marked on Figure 2 21 were reported in the June 2011 Bridge Inspection Report, and all in the welded connection between 22 the lower end of the cross frame (Figure 3) connection plate and the girder bottom flange of the 23 southbound superstructure. Figure 4(a) shows one of the four crack locations at G3B2D3 (Girder 3 24 Bay 2 Diaphragm 3). Therefore, only the southbound superstructure will be discussed in the 25 following sections. 26

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Field Test and Results 28

The field test of the I-270 Bridge over Middlebrook Road with active fatigue cracks was conducted 29 through a Wireless Integrated Structural Health Monitoring (ISHM) System. This smart bridge 30 condition monitoring system, termed the ISHM system, features a number of technology 31 innovations, including remote sensing capability, piezo paint acoustic emission sensors, wind and 32 solar based energy harvesting devices to power the sensor network, high-speed wireless sensing 33 ability and advanced data analysis methods for remaining life estimation of aging bridges. 34 Through successful advancement and commercialization in the state-of-the-art technology of 35 remote infrastructure sensing, the ISHM system is promising to reduce life cycle costs while 36 significantly maintaining the sustainability of the highway infrastructure in the US. 37

Instrumentation Plan 38

The main data acquisition systems used in this test consisted of a PXI-based data acquisition 39 system by National Instruments, which was used for data collection by the BDI strain transducers, 40 string pots and AE sensors, and a multi-channel data acquisition equipment CR5000 manufactured 41 by Campbell Scientific, Inc., which was used for the extra BDI strain transducer. Types of sensors 42 used in this project were: 1. piezoelectric paint AE sensors; 2. wireless accelerometers; 3.laser 43

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sensor; 4. ultrasonic distance sensors; 5. BDI strain transducers; and 6. string pots. Sensors were 1 strategically placed where the cracks on the SB bridge were identified and their related strain, AE 2 or supplemental data can be collected by the data acquisition system and later validated by the FE 3 models. The instrumentation plan is shown inFigure 2.Girder displacement and stress range 4 records due to truck traffic were part of the field measurements in this study. 5

Vibration Response 6

A total of four wireless accelerometers were used to monitor the vibration responses of the bridge. 7 Wireless sensors were installed on four girders (Girders 2 to 5) and acceleration data was acquired 8 at 100 Hz sampling rate synchronically. The acceleration data was used to provide modal 9 frequency information that was used to calibrate the finite element model of the bridge. The 10 fundamental frequency thus measured is 3.22 Hz, which was very close to the value of the first 11 vertical mode from the finite element analysis of 3.24 Hz discussed in following sections. 12

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1 FIGURE 1 - Cross section with lane positions. 2

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1 FIGURE 2 - Crack locations and sensor placements on the framing plan. 2

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FIGURE 3 - Cross frame detail. 2

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(a) Details at G3B2D3 (b) Details at G3B3D3 4

FIGURE 4 - Crack locations and sensor placements. 5

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Bridge Deflection 1

Both laser sensor and ultrasonic distance sensors were used to measure the dynamic deflection of 2 the bridge. Only one laser sensor and one ultrasonic distance sensor were used each time. The 3 measured deflection value from the laser sensor agreed well with the string pot, and its accuracy 4 was also validated by the fundamental frequency indicated by Fast Fourier Transform (FFT) of the 5 laser sensor measured deflection data. The measured maximum deflection of the I-270 Bridge over 6 Middlebrook Road under traffic loading is summarized in Table 1. 7

Table 1 - Maximum Deflection Measured by Laser Sensor 8

Girder Number 3 4 5

MaxD (in) 0.2598 0.2717 0.2480

Stress 9

Cracks always occur in the direction essentially perpendicular to the direction of principal tensile 10 stress. In order to assess the driving force of the fatigue cracks in the connection welds, strain 11 gages were placed vertically on the connection plate just beyond the tip of the existing crack. 12 Strain gages were also placed longitudinally on the girder flanges to correlate with the occurrence 13 of vehicular loads. For comparison with the results from analytical methods, field testing is the 14 most accurate approach since no assumptions need to be made for uncertainties in load distribution 15 such as unintended composite action between structural components, contribution of nonstructural 16 members, stiffness of various connections, and behavior of the concrete deck in tension. The actual 17 strain histories experienced by bridge components are directly measured by strain gages at the 18 areas of concern. The effects of varying vehicle weights and their random combinations in 19 multiple lanes are also reflected in the measured strains. 20

BDI 1‐4 strain transducers were placed on both sides of the connection plates while BDI 5‐ 21 8 strain transducers were placed on the top and bottom flanges on Girders 3 and 4 (Figure 2). 22 Figure 5 shows the measured stresses on the flanges and connection plates, respectively. The 23 maximum stress measured on the bottom flange was 1.604 ksi in tension for BDI 3215 on the 24 bottom flange of Girder 3 due to regular traffic loading, which was very low comparatively. As for 25 the connection plates, the maximum stresses were 16.18 ksi in tension for BDI 1641 on Girder 3 26 and 16.1 ksi in tension for BDI 1644 on Girder 4 (Figure 5). 27

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FIGURE 5 - BDI strain transducer measurements of connection plates and flanges (positive 2 indicates compression; 1641 G3 cracked side; 1642 G3 uncracked side, 1643 G4 uncracked 3 side and 1644 G4 cracked side). 4

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FINITE ELEMENT MODELING 6

Traffic Loading 7

The traffic data that were used to simulate traffic flow were the time varying vehicle count data 8 from the Internet Traffic Monitoring System operated by Maryland Department of Transportation 9 State Highway Administration [5], by the Highway Information Services Division, Maryland State 10 Highway Administration. The Traffic Monitoring System program has been responsible for the 11 collection, processing, analysis, and management of Maryland highway traffic data since 1997. 12 Maryland’s Traffic Monitoring Program includes 79 permanent continuous Automatic Traffic 13 Recorders (ATRs) counting traffic continuously throughout the year, and over 3,800 short term (48 14 hour) program count locations throughout the state, with data taken during the week on either 15 Tuesday and Wednesday or Wednesday and Thursday to reflect typical weekday travel patterns. 16 The Traffic Monitoring System Program covers almost the entire area of Maryland and monitors 17 most of the arterials, freeways, and interstates. Apparently, using traffic data from the Traffic 18 Monitoring System Program to generate truck loading in Maryland is accessible and reliable. 19

The simulation procedure can be summarized in four steps. (1) Build the simulation 20 network in TSIS 5.1 [6] around the MD Bridge No. 1504200 I-270 over Middlebrook Road based 21 on the background map obtained from Google Map. (2) Use the time varying vehicle count data 22 collected from nearby detectors as the input data for the simulation model. The truck count data are 23 converted to truck percentage. (3) Install three loop detectors at the bridge in the created 24 simulation network, one for each lane in order to record the speed, type and passage time of the 25 detected vehicles. (4) Run the simulation. The passage time, speed and lane traveled by the trucks 26 could be recorded, just like virtual weigh-in-motion data. 27

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Bridge Global Model 1

To investigate the fatigue performance of the bridge, a three-dimensional finite element model was 2 developed for linear-elastic structural analyses using the CSiBridge [7], as depicted in Figure 6. 3 The model of the southbound superstructure consisted of eight I-girders. The concrete deck, the 4 eight I-girders, and connection plates which connected cross-frames to the girders were modeled 5 by shell elements, while all the cross-frames were modeled by spatial frames along their 6 center-of-gravity. Special link members were defined to connect girder elements and concrete deck 7 elements at the actual spatial points where these members intersect. The translations in the x-, y-, 8 z-directions were fixed at the abutments to represent the actual characteristics of support and 9 continuity. It is very complicated to establish a finite element model of a large practical structure 10 for fatigue damage analysis, as the finite element model should embody the sectional properties of 11 structural members. Moreover, in considering that fatigue damage is a local failure mode and often 12 occurs around welded regions, a global model with refined meshing around the welded connection 13 between the connection plats and the bottom flanges was constructed for analysis. 14

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(a) Isometric view of FEM for I-270 Bridge. 17

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(b) Zoom-in view (refined meshing around the welds). 19

FIGURE 6 - Finite element model of I-270 Bridge in CSiBriddge. 20

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Convergence Test 1

The accuracy of a finite element analysis depends on the mesh size of the elements. Basically, the 2 smaller size of the elements, the greater the accuracy of the analysis. However, the desire for 3 increased calculation accuracy should not significantly compromise the computational time. A 4 convergence test in finite element analysis is a procedure used to determine appropriate mesh size 5 for a model. The measurement of a finite element model’s mesh size should depend on the purpose 6 of the model. Since this bridge model is to investigate the vertical stress or shear stress in the 7 cracked connection weld, then it needs to have a very fine mesh in the connection area but needs to 8 also transit gradually to coarser meshes because otherwise the model would become unnecessarily 9 too large. A more uniform mesh may then be used along the rest of the bridge length for all the 10 girders. However, there are multiple parameters related to the accuracy of a two-dimensional or 11 three-dimensional finite element model, including the dimensions and aspect ratios of the elements 12 for the girder top flange, bottom flange, and web, as well as the bridge deck. 13

To simplify the convergence test for these finite element models of the I-270 Bridge over 14 Middlebrook Road, a consistent refined mesh around the weld region was employed in all the 15 models, and the maximum element size was used in control the uniform mesh along the bridge 16 longitudinal length for all the girders and the deck. The determination of the first natural frequency 17 was used as the measurement during the convergence test. As the maximum mesh size changed 18 from 1000 in to 0.5 in, the results of the first natural frequency gradually increased from 2 Hz to 19 3.20 Hz. The results of the first natural frequency were all beyond 3 Hz when the maximum mesh 20 size of the finite element models was smaller than 200 in, which means that the error rate of the 21 first natural frequency was under 6.25%. When the maximum mesh size was equal to or less than 22 50 in, the results of the first natural frequency were accurate enough with an error rate less than 2%, 23 and was therefore used as the basis for the selection of an accurate finite element mesh in 24 CSiBridge. 25

Modal Analysis 26

Modal analysis is used to determine the vibration modes of a structure. These modes are useful to 27 understand the behavior of the structure. They can also be used as the basis for modal 28 superposition in response-spectrum and modal time-history load cases. An eigenvector analysis 29 was used to determine the undamped free-vibration mode shapes and frequencies of the system. 30

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(a) Mode shape 1 (first torsion) (b) Mode shape 2 (first vertical) 32

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(c) Mode shape 3 (second torsion) (d) Mode shape 4 (first lateral) 2

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(e) Mode shape 5 (second vertical) (f) Mode shape 6 (third torsion) 4

FIGURE 7 - Mode shapes of I-270 Bridge over Middlebrook Road in CSiBridge. 5

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As a matter of interest, the first six mode shapes of torsion, vertical and lateral modes are 7 shown in Figure 7. To validate the finite element models, experimental data from the field test and 8 numerical results from CSiBridge were studied. In the numerical study, the bridge was only 9 subjected to dead load. The results obtained from the finite element model and field measurements 10 were compared, and the differences of most of the compared frequencies were less than 6%, which 11 was considered acceptable for the finite element analysis. All the mode shapes matched well with 12 each other. Therefore, the CSiBridge model was considered to be reasonably accurate for the 13 purposes of this study. 14

Stresses by Simulation 15

Possible driving forces for the fatigue cracks shown in Figure 4 would have to be vertical tensile 16 stress, horizontal shear stress, or the principal tensile stress due to their combined actions, along 17 the connection welds. Live load induced stresses from the welded connections between the 18 cross-frame connection plates and the girder bottom flanges were extracted in the refined portion 19 of the finite element models. A total of four different traffic loading cases obtained from the traffic 20 simulation were studied as described below and key results summarized in Table 2. For all the four 21 cases analyzed, the longitudinal positions of trucks remained the same as for the previous 22 deflection studies. 23

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Table 2 - Stresses in Cross Frame Connection Plate-to-Girder Bottom Flange Connections at 1 G3 without Dynamic Impact (FE Resutls) (unit: ksi) 2

Time Period Max Vertical Stress Max Shear Stress Max Principal StressMidnight 6.665 2.165 7.629

Early Morning and Night 7.586 2.563 8.70 Morning Peak 12.94 4.327 14.84

Noon to Evening 7.905 2.664 9.061

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There were certainly many live load cases that could have produced significant tensile 4 stresses in the connections of concern. The simulated truck loading contained most of the possible 5 truck loading patterns. Magnitudes of tensile stresses in the connection plates depend on the 6 magnitudes and positions of the wheel loads of crossing vehicles. The stresses listed in Table 2 are 7 for illustration and are taken from the connection plates at Girder 3 for the four different time 8 periods. A comparison of live load cases for the four different time periods suggest that live loads 9 during morning peak may have caused the highest tensile stress of 12.94 ksi in the connection of 10 concern. All the shear stresses in the connection welds were much lower than the vertical stresses 11 at the same spot during each time period. 12

Cause of Fatigue Cracks 13

Connection Plate Configuration 14

The results of the finite element analysis matched with the field test data; all the cracks were 15 located on the western sides of the connection plates. The vertical stress near the welded edges of 16 the connection plates followed the same pattern; the western sides of the connection plates were 17 under tension, and the eastern sides of the connection plates were under compression. To further 18 discuss the cause of this phenomenon, a series of controlled FEM tests were established for 19 comparison study. 20

According to the design drawing, cross-frame connection plates and bearing stiffeners 21 were to be normal to the girders and connection plates were tobe bent as required. Therefore, for 22 the original FE model, all the connection plates were normal (90 degree) to the girders and the 23 cross-frames are parallel to the two abutments with a skew angel of 76 degree. For the controlled 24 model, all the connection plates were parallel to the cross frames with the same skew angel of 76 25 degree. 26

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28 FIGURE 8 - Skewed (right) and non-skewed (left) connection plates. 29

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Bracing System Configuration 1

The K-type bracing system was modeled for studying the influence of the bracing system 2 configuration on the stress distribution in the connection plates. The K-type cross-frame without 3 top chord was modeled in the original FE model, while the K-type cross-frame with top chord was 4 modeled in the controlled model. The cross section of the diagonal and bottom chords was 5 employed for the additional top chords. All the models were subjected to the same live load case. 6 The live load case was defined as an HS20 truck in the right traffic lane passing across the bridge 7 from north to south at the limited speed of 55 mph. The vertical stress at the crack location (Girder 8 3 Diaphragm 3) and the axial forces in the top chord located at Diaphragm 3 Bay 2, directly 9 connecting with the crack side, were analyzed and are shown in Table 3. Maximum vertical 10 stresses in the model with the non-skewed connection plates were much higher than the stresses in 11 the model with the skewed connection plates. The maximum axial forces in the models during the 12 load time history analysis were quiet small; the values were only 3.47 kip and 1.12 kip. The values 13 of maximum vertical stresses did not change much due to the addition of a top chord. It 14 demonstrates that the connection plate configuration has a significant influence on the stress 15 distribution in theconnection plates, while the top chord of K-type bracing plays a negligible role 16 in this situation. Further, results show that X-type or K-type bracing made no difference on the 17 vertical stress at the crack location. 18

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FIGURE 9 - K-frame without top chord (left) and K-frame with top chord (right) 21

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Table 3 - Maximum Vertical Stress and Axial Force through Simulated Numerical Analyses 23 Connection Plates

Configuration Bracing System Configuration

Max Axial Force (kip)

Max Vertical Stress of Crack location (ksi)

Non-Skewed Connection Plats

K-frame without top chord - 13.50 K-frame with top chord 3.47 12.66

Skewed Connection Plats

K-frame without top chord - 0.33 K-frame with top chord 1.12 0.30

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The measured high vertical tensile stress around the connection plate welds was proven 25 caused by the configuration of the connection plates instead of the configuration of the 26 cross-frames. The connection plates, which were bent to be parallel to the skewed abutment, 27 induced torsion in the connection plate welds. Differential displacements between the girders 28

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caused one diagonal cross frame to be in tension and the other diagonal to be in compression. 1 Measured vertical tensile stresses from field tests up to 16.1 ksi in the connection plate explains 2 why fatigue cracks have occurred at their connections to the girder bottom flange. Girders 3 and 4 3 are located under the slow moving lane which most heavy trucks are using while Girders 1 and 2 4 support a shoulder and thus large differential deflections typically occur between Girders 2 and 3 5 (with up to 0.5” to 0.75” vertical deflections due to observed live load). The connection plate 6 configuration is a key factor in the stress distribution that results in the connection plates. 7

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CONCLUSIONS 9

The passage of trucks on the bridge deck can cause vertical tensile stresses in the welded 10 connections between cross-frame connection plates and girder bottom flanges. These stresses were 11 highest at the outer edge of the connection plate where all the existing four fatigue cracks on the 12 I-270 Bridge over Middlebrook Roadwere located. Girder 4 located at the center left of the middle 13 traffic lane, and Girder 3 located at the center right of the right traffic lane, are the most critical 14 locations for the bridge deflections and the resulting stresses. 15

The live load induced stresses in the connection plates were localized around the welded 16 connections and would not be anticipated to spread from the bottom to the top of connection plates. 17 At the same face of the connection plate, both tensile and compressive stresses were observed at 18 the symmetry positions around the girder web. The cracked side of the connection plates was 19 always under tensile stress, while the uncracked side was always under compressive stress during 20 each time period. At the same spot of the cracked side, the north face and the south face sustained 21 the same, but opposite, stresses. The high vertical tensile stress around the connection plate welds 22 was proven caused by the configuration of the connection plates instead of by the configuration of 23 the cross-frames. The connection plates, which were bent to be parallel to the skewed abutment, 24 induced torsion in the connection plates welds. The connection plate configuration is a key factor 25 in the stress distribution that results in the connection plates. 26

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ACKNOWLEDGMENT 28

This work was partially sponsored by the US Department of Transportation’s Office of the 29 Assistant Secretary for Research and Technology (USDOT/OST-R), under The Commercial 30 Remote Sensing and Spatial Information (CRS&SI) Technologies Program. This support is 31 acknowledged and greatly appreciated. 32

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REFERENCES 34

1. Craig Quadrato, Weihua Wang, Anthony Battistini, Andrew Wahr, Todd Helwig, 35 Karl Frank, and Michael Engelhardt. Cross-Frame Connection Details for 36 Skewed Steel Bridges. Publication FHWA/TX-11/0-5701-1. Texas Department of 37 Transportation, 2010. 38

2. Mertz, DR. Designers’ Guide to Cross-Frame Diaphragms. American Iron and 39 Steel Institute, Washington, D.C, 2001. 40

3. H. L. Hassel, C. R. Bennett, A. B. Matamoros, and S.T. Rolfe. Parametric Analysis 41

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of Cross-Frame Layout on Distortion-Induced Fatigue in Skewed Steel Bridges. 1 Journal of Bridge Engineering, Vol. 18, 2013, pp. 601-611. 2

4. Todd Helwig and Joseph Yura. Steel Bridge Design Handbook: Bracing System 3 Design. Publication FHWA-IF-12-052 - Vol. 13. FHWA, U.S. Department of 4 Transportation, 2012. 5

5. Internet Traffic Monitoring System. Maryland Department of Transportation State 6 Highway Administration. 7 http://shagbhisdadt.mdot.state.md.us/ITMS_Public/default.aspx. Accessed Jul. 29, 8 2015. 9

6. TSIS Unser’s Guide. McTrans Center. Department of Transpiration Federal Highway 10 Administration: Washington, D.C, 2003. 11

7. CSiBridge. Integrated 3D Bridge Design Software. Computer and Structures, Inc: 12 Berkeley, CA, 2010. 13