Determination of Stress Range for DE Bridge #771 Using Staad Pro 2004
Greg Callahan University of Missouri-Columbia
Advisor: Prof. Mertz
Submitted to: NSF-REU, University of Delaware Civil Engineering Dept.
August 12, 2005
Table of Contents Table of Contents ................................................................................................. 2 Abstract ....................................................................................................................... 4 Introduction................................................................................................................. 5 Background ................................................................................................................. 6 Methods and Procedures ........................................................................................... 15 Data Analysis and Discussion................................................................................... 22 Conclusion ................................................................................................................ 24 Acknowledgements................................................................................................... 25 References................................................................................................................. 26 Appendix A....................................................................................................................... 27 Appendix B ....................................................................................................................... 29 Load Case 1....................................................................................................................... 30 Load Case 2....................................................................................................................... 31 Load Case 3....................................................................................................................... 32 Load Case 4....................................................................................................................... 33 Load Case 5....................................................................................................................... 34 Load Case 6....................................................................................................................... 35 Load Case 7....................................................................................................................... 36 Load Case 8....................................................................................................................... 37 Load Case 9....................................................................................................................... 38 Load Case 10..................................................................................................................... 39 Appendix C ....................................................................................................................... 40 Overpass at Shipley Road Plan and Elevation.................................................................. 41 Overpass at Shipley Road N. B. L. Framing Plan ............................................................ 42 Overpass at Shipley Road N. B. L. Deck and Approach Slabs Plan and Bar Schedule ... 43 Overpass at Shipley Road N. B. L. and S. B. L. Sections and Details ............................. 44 Appendix D....................................................................................................................... 45 Load Definition................................................................................................................. 46 Moving Load Generation.................................................................................................. 48 Final Generated load ......................................................................................................... 51 Appendix E ....................................................................................................................... 52 Transverse Welds.............................................................................................................. 53 Northern Side ............................................................................................................ 53 Southern Side ............................................................................................................ 54 Longitudinal Welds........................................................................................................... 55 Girder One ................................................................................................................ 55 Girder 2 ..................................................................................................................... 56 Girder 3 ..................................................................................................................... 57 Girder 4 ..................................................................................................................... 58 Girder 5 ..................................................................................................................... 59 Girder 6 ..................................................................................................................... 60
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Abstract The goal of this study is to determine stress ranges felt on Delaware Bridge #771. This bridge contains two fatigue-sensitive details experiencing different stress ranges. The determination of these stress ranges will be done using the structural analysis computer program Staad.Pro 2004. In order to apply Staad, a model of DE Bridge #771 is generated and analyzed within the computer program. Ultimately, this study determines if the fatigue-sensitive details are exposed to high enough stress levels to cause fatigue failure and if so what the remaining fatigue life of each detail would be. The concepts and methods used in analysis of the bridge come from studies conducted by Dr. John Fisher of Lehigh University, AASHTO, and the NCHRP. Hopefully this study will set forth a methodology that is easily understood and reproducible so that others can apply similar methods of analysis to other bridges.
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Introduction Bridge fatigue can be a serious problem. If ignored, fatigue can cause sudden and total failure of a bridge. Fatigue failure of a detail can occur at stress levels far below the ultimate strengths of that material. Fatigue failure is dependent on time and frequency of loading; moreover, failure occurs due to the repeated cyclic loading of a structure. Fatigue failure is an important consideration in older bridges that have experienced a larger number of loads cycles and are more susceptible to failure at lower stress ranges than newer bridges that have not been exposed to as many cycles. The time it takes for a structure to fail due to fatigue is called the fatigue life. Fatigue life can be calculated throughout the life of a structure. Remaining fatigue life is the time remaining until fatigue failure is Bridge plans provide the necessary details for modeling in the computer program Staad. Pro 2004. This program can determine the maximum and minimum stresses each girder experiences. From these values a stress range can be determined and this can be used to determine the remaining fatigue life of that detail. There are approximately thirty-six bridges in the span of I-95 from Newark, Delaware to Philadelphia, Pennsylvania if both directions are considered. The majority of these bridges are relatively new so there is no immediate risk of fatigue failure, but determining the stress ranges of the bridges would allow the remaining fatigue life to be calculated providing the Delaware Department of Transportation with a predicted time of failure so the appropriate precautions could be taken in the future. Due to the relatively short time I spent at the University of Delaware, stressrange calculations for all thirty-six bridges were not possible. Instead, Delaware Bridge # 771 was chosen for analysis. Bridge # 771 is a simply supported three span bridge that
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runs over Shipley Rd in the direction of Philadelphia from Wilmington. This bridge was chosen because it has fatigue sensitive cover plates, and is very similar to a number of highways overpass bridges. Hopefully, it will be able to act as a case study for future analysis of similar bridges on I-95 and other highways as well as aid in further studies on the stretch of I-95 being analyzed.
Fig 1- Delaware Bridge #771 to Philadelphia on I-95 North Bound
Background In order to understand why fatigue analysis is important, the nature and behavior of fatigue failure must first be addressed. Fatigue is the process of cumulative damage in a benign environment that is caused by repeated fluctuating loads and, in the presence of an aggressive environment, is known as corrosion fatigue (Barson & Rolfe 1999). Fatigue is a property that can be affected by a number of factors. The state of stress carried by the structure, the geometric properties of the design, and the environment all can influence the fatigue resistance of a structure (Barson & Rolfe, 1999). For this study
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of Delaware Bridge #771, the geometric properties of the bridge design proved to be the largest factor for fatigue. Fatigue is an issue for fracture-critical details such as the welded cover plates found on Bridge #771. As set forth by the AASHTO Manual for Maintenance Inspection of Bridges, the details on bridges like bridge #771 are inspected at two-year intervals for fatigue analysis. However, neither the AASHTO Manual for Maintenance Inspection of Bridges, nor Standard Specifications for Highway Bridges yielded accurate or realistic fatigue life approximations (NCHRP 299, p 5). Due to the need to have a standard, accurate, and reproducible method to determine the remaining fatigue life in bridges, the National Cooperative Highway Research Program, NCHRP, produced report 299. This report covers procedures for fatigue evaluation of existing steel bridges, and how to design for acceptable fatigue lives in new steel bridges. The remaining fatigue life of a bridge is determined by analysis of bridge details. A table of these details and classifications can be found in Appendix A. These details create points of stress concentrations that can, and often do, result in large stress ranges ultimately causing fatigue failure. The type of stress these details are subjected to also influences the degree of fatigue failure. In order for a bridge detail to be considered a fatigue detail, it must be exposed to applied tensile stresses (Mertz). This is an extremely important concept to address before any fatigue analysis takes place. The fatigue details on Delaware Bridge #771 consist of longitudinal welds and transverse welds that attach cover plates to the bottom flange of the girders in the middle portion of each span. Because these details are located on the bottom flange of a simply supported beam, they experience tensile stress. This can be assumed because of how stresses are distributed in
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an I-Beam girder. The top flange will support compressive stresses while the bottom flange will support the tensile forces.
Fig 2 - Cross-Section of a sample W36X135 beam found in Delaware Bridge #771. These beams have cover plates, however, in this rendering the plate in exaggerated for viewing purposes.
As seen in Fig 2, the cover plate clearly falls below the neutral axis of the I – Beam. The added mass to the beam increases the moment of inertia of the beam and allows the girder to support larger moments.
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Fig 3- Moment diagram generated from the structural analysis program Staad.Pro 2004.
Figure two illustrates the moment diagram for one W36X135 girder with a bottom cover plate. The load on the girder is a HS-15 truck, a standard fatigue truck as set forth by the AASHTO Guide Specifications for Fatigue Evaluation of Existing Steel Bridges (1990). The model was created in the structural analysis program Staad. Pro 2004. The sign convention in Staad is opposite for moment diagrams, so according to the structural analysis sign convention the maximum moment for figure two is a positive 3906 kip-in. Another interesting property of Staad is that while the moment diagrams produced are off by a factor of negative one, the diagrams do accurately reflect the deformed shape of the beam under the set loading conditions. So, from figure 2 it can be concluded the bottom flange of the beam is indeed subjected to tensile stress and therefore, the bottom flange cover plate welds are fatigue - sensitive details. This means that Delaware Bridge #771 is in danger of experiencing fatigue failure.
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Fatigue failure was first seen around 120 years ago by Wohler who noticed stress concentrations and sharp angles in axle configuration of railway rolling stock that led to failure well below the ultimate strength of the material (Barsom 16). Studies for weld examinations in the 1930’s and later in WWII laid the initial groundwork for fatigue design in the North America and led to the fatigue test program sponsored by the National Cooperative Highway Research Program at Lehigh University ( Barsom 16). Before the establishment of the NCHRP fatigue analysis was very limited based only on small specimens and on a limited quantity of test data, this is why many existing bridges built before 1970 have large amounts of fatigue cracking (Barsom 16). Since the establishment of a fatigue analysis program by the NCHRP, fatigue failure has become less and less of a problem due to standardized testing methods and continual research yielding new information on how to predict remaining fatigue life. This study deals with the stress ranges experienced by girders due to loading. The stress range a girder is subjected to is a key factor in the remaining fatigue life of that girder. The equation below is the equation used to determine remaining fatigue life as given in NCHRP 299.
The variables above are given in the table on the next page.
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Variable Yf f K Ta C Rs
Sr a
Represents Finite remaining Fatigue Life Factor to account for difference betwe allowable S-N curves: f = 1 for safe li mean life Detail constant determined by the category of the fatigue detail Estimated lifetime average daily truck volume Cycles per truck passage: assumed C = 1 unless specified otherwise Reliability value associated with calculation of stress range: to determine remaining mean life Rs = 1 Stress range, values determined in this study Age of bridge in years
Table 1 – explanation of the variables found in NCHRP 299 remaining fatigue life equation
In order to determine if the equation above is needed to find the remaining fatigue life, it is it must be determined if the details are exposed to stresses larger than their stress threshold values. These detail classifications and threshold stresses were determined by Dr. John Fisher of Lehigh University in the late 1960’s and early 1970’s. Fisher recognized that different types of connections, geometries, and materials used in construction would fail at different stresses for the same amount of cyclic loading. In response to this discovery, he developed a standardized characterization of eight fatigue details. These details were each developed using a 95 % confidence limit (Fisher). This means that many trials were conducted, and the failing points were analyzed. After the analysis of the data was conducted, the line that 95 % of the failures occurred at or above was found to be the stress threshold. The dashed line in Fig 4 illustrates this limit because almost all of the failures occur above or on this line. 11
Fig 4 - Example of the 95 % confidence limit method used by Dr. John Fisher of Lehigh.
If the details were subjected to stresses below this confidence limit it can be assumed that they have an infinite theoretical fatigue life, meaning they will not fail due to fatigue. If they are exposed to stresses above the threshold limit, the detail will have a finite fatigue life and once the appropriate number of cycles has been applied fatigue failure will occur. The details Dr. Fisher established ranged from the least fracture - critical detail (A), to the most fracture-critical (F) (Fisher). An interesting aspect of Fisher’s study is that even though his work was conducted over thirty year ago, his detail classification system is
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still used today. AASHTO adopted the system and made one rather sizeable change. The category F was not easy to understand and some problems occurred with accurately recognizing and analyzing the details. To remedy this, AASHTO renamed the category E’ and set forth parameters that were easier to understand and apply. These details along with the corresponding stress ranges can be seen in table 2 below. The table clearly shows that class A details can be exposed to much more stress on a consistent basis than details in the E or E’ classification.
Detail Classification
Stress Threshold (Ksi)
A
24
B
16
B’
12
C
10
C’
12
D
7
E
4.5
E’
2.6
Table 2 – AASHTO stress thresholds for fatigue sensitive details.
The particular classifications of details this study will examine are Class B and Class E with stress thresholds of 16 ksi and 4.5 ksi respectively. The reason that this study is interested in details B and E is they are the fatigue sensitive details found on DE Bridge #771. The Bridge is composed steel girders with cover plates on the bottom flange. On top of these girders sits an 8 in. concrete deck.
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The deck and the girders act compositely. For a more detailed description of DE Bridge #771 look in Appendix C. Class B and E details can be found on the welds which attach the cover plate to the bottom flange. The transverse welds are class E details and the longitudinal welds are class B details. Figure 5 shows the actual welds on bridge #771.
Fig 5 – Shows Class E and Class B fatigue sensitive details on DE Bridge #771
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Methods and Procedures The main task of this study was to correctly model DE Bridge # 771 in the Staad. Pro 2004 computer program, Staad, so the stress ranges found would be correct. Initially, the entire bridge was modeled in Staad. However, this did not seem to be a
Fig 6 – Initial model of entire bridge
practical process to determine the stresses felt by the girders. Each span of the bridge is simply supported so, essentially the bridge can be considered as three individual spans. It was assumed each span acts independently of the other two spans. In accordance with this observation, a single span was chosen for modeling and analysis. This single span was the longest span on the bridge. It was selected because it will carry the largest moment, and thus be exposed to the highest levels of stresses. The modeled span had a length of sixty – six feet and was composed of six W36X150 rolled girders, ten MC18X42 steel channel diaphragms, an 8-inch concrete deck, and W40X655 steel members. The 40X655 members acted as rigid connectors between the steel girders and the concrete deck.
Fig 7 – Initial span model with truckload applied
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Fig 8 – Axle load and spacing of an HS-15 truck
Once the span was selected and modeled the loading needed to be applied. In order to do this AASHTO procedures were followed. AASHTO calls for an HS-15 truck to be used in fatigue design and evaluation. Figure 7 shows the initial position of the truck loading (the red outline) on the span model. It should be noted that the truck is placed on the right side of the bridge. The placement represents the most likely truck traffic. On actual highway bridges, the outer lanes undergo a much higher frequency of truck loading than the inner lanes. This placement acts to simulate real – world traffic conditions. Figure eight shows the axle loads and spacing of the HS-15 truck used. The truck needed to be applied at multiple longitudinal positions on the span to simulate an actual test. This could be done in Staad using the load generation options. For a detailed description of the application and definition of the HS – 15 truck loading consult Appendix D. Simulating a moving load across the modeled span was not the only problem encountered during the modeling process. Instability issues became quite frustrating as
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analysis of the model was conducted. Originally, the girders were modeled in three pieces. Two smaller sections of ten feet and one forty-six foot section. The girders were modeled this way because Staad was not able to model one member with a cover plate covering only a portion of the member. Figure nine shows how the members were modeled.
Fig 9- Initial modeling of cover plate girders
However, once the diaphragms were attached instabilities were recorded at the joints where the diaphragms met the girders. While investigating the instability issue, a discovery took place. The problem was not one of stability, rather a nodal problem with the connections of the members. Staad uses defined points called nodes to serve as data points for defining members, plates, different structures, etc. Members that composed the girder sections of the span did not terminate and begin at the nodes the where the diaphragms were connected. Because of this, Staad was not able to register the two components were even connected. Once the problem was realized the original forty-six girder section was broken down into five smaller sections shown in figure ten.
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Fig 10 – Final modeling of girders with cover plates
This new method of producing the same girders fixes the instability problems seen in earlier trials of modeling. The girder – diaphragm connections were not the only place instability issues arose during modeling. Once the steel configuration was modeled and stable under loading, the concrete deck had to be added to the model. This was done using plate geometry in Staad. The first attempt to model the deck simply consisted of making one large plate to sit on top of the steel sections. This method did not work and instability problems as well as a non-composite action resulted under loading. The next attempt proved to be quite successful. It entailed utilizing a larger number of nodes to serve as data points in Staad. The deck was modeled as a synthesis of twenty smaller plates that act together to simulate on large plate that covers the entire modeled span. The plate elements were then given the thickness of eight inches and assigned concrete properties.
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Figure eleven shows how the twenty smaller plates were configured to produce the concrete deck.
Fig 11- Final configuration of modeled concrete deck
Once the deck and the steel components of the bridge were modeled correctly, the two sections needed to be connected in a manner that would result in composite action of the girders and deck. The real DE Bridge #771 acts compositely so the generated model needed to illustrate the trait as well. Many attempts were made to create a composite model. The first was simply placing the deck on top of the steel without node connections. This resulted in non-composite action and in the deck passing through the webs of the steel girders. To remedy this mistake, the concrete deck was offset 1.495 ft, which translates to the distance from the centroid of the girder’s cross section to the centroid of the deck’s cross section. This attempt saw the deck placed correctly on the beam, but composite action still did not occur when the model was loaded. Finally, robust steel members were placed at 16.5 ft along each girder to act as rigid connectors between the steel and the deck. The members used were W40X655 beams running in the vertical direction. These beams benefited the model in two ways; first, they proved a
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means to connect the deck to the steel and second, they created many nodes along the girders to serve as more data points for analysis. Figure twelve shows a threedimensional rendering of how the connectors were used.
Fig 12 – W40X655 beams used as rigid connectors in model
As the figure above shows the connectors were very large beams. This was extremely important because deformation of the connectors would throw off the stress ranges determined from the model. Stiff members were selected due to the large values of stiffness they posses. Once the rigid connectors were added, the model reflected composite action. For in depth illustrations of stress distribution experienced by the deck during each of the ten different load cases please refer to Appendix B. With the model completed and simulating the actual DE Bridge #771, analysis of the model needed to take place. However, the bridge was composed of six longitudinal girders only one of which was loaded directly by the simulated HS- 15 truck. Originally, it was thought that distribution factors would have to be calculated for analysis of all the girders in the deck. On the first analysis run of the completed model, an interesting
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discovery took place. Staad distributed the truckload over the girders for each generated load case. At each of the ten different positions of the truckload green arrows signified where the load was being distributed.
Fig 13- The load distribution of the HS-15 truck by Staad for the first and fifth load case
As figure thirteen illustrates the initial position of the truck stays consistently outlined as red axle loads while the actual position and distribution of the generated load is shown by the green arrows. For detailed positioning distribution of each generated load please consult appendix B. At this point of the project the loads were correctly defined and placed on the structure, and the model correctly simulated DE Bridge #771 Stress analysis of the simulation could finally take place.
Fig 14 – Three-dimensional renderings of the model used for stress range analysis
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Data Analysis and Discussion With the model completed the stresses felt in the steel girders that contained the fatigue sensitive details needed to be determined. Staad proved to be quite helpful in completing this task. After running an analysis, the “beams” tab was selected and from that menu, the “stresses” option was chosen. In the “stresses” analysis screen any point along any girder in the model could be selected and the stress felt by that girder during any of the ten load cases could be accessed. This option made data collection very easy. For the transverse welds along the ends of the cover plates the stresses were recorded at the point the plate and bottom flange are welded together. This point was the obvious choice since the weld itself is the fatigue-sensitive detail. Staad allowed exact positioning of this point on the cross-section of the girders. Figure 15 shows form where on the girder the stresses were recorded.
Fig 15- Location the transverse weld stresses were taken
Stresses were taken from both ends of all the girders that had cover plates so twelve readings in all. The stresses at each end of the six girders that had cover plates were collected from the model and placed into the Microsoft Excel program. From there graphs were generated to find the stress ranges and see if the stresses felt exceed the threshold stress of the detail. These graphs can be seen in Appendix E. The stresses felt by the Class E
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details in the bridge simulation did not exceed the threshold stress of 4.5 Ksi. All other trends displayed by the graphs were to be expected. The details located on the right side of the bridge experience much greater stresses than those on the left. This was due to the placement of the load on the right hand side of the bridge to simulate truck traffic.
Fig 16 – Placement of largest stresses felt in transverse welds
In addition to the stresses felt by the class E transverse weld, the stresses in the longitudinal welds were also determined. The longitudinal welds on the girders are a class B fatigue sensitive detail so it has a higher stress threshold of 16 Ksi. Stress readings were taken along the six beams containing the cover plates at 0, 11.5, 23, 43.5, and 46 ft using Staad.
Fig 17- Girders that were analyzed for stresses felt in longitudinal welds
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Once the data was colleted it was again exported to Excel and graphs were generated to determine the stress ranges. These graphs can be seen in Appendix E. According to the graphs, girders one and two experience the largest stress from the generated loads. Because of the truck placement, this is expected. The maximum stress felt by any girder does not come close to the threshold stress of 16 Ksi. Therefore, the results of the study show that the threshold stress of both class B and class E details is not exceeded.
Conclusion This study showed that DE Bridge #771 has a theoretical infinite fatigue life. Both fatigue-sensitive details are not exposed to stresses exceeding their respective stress thresholds. The equation outlined in NCHRP 299 does not need to be applied to either of the details in this study because the fatigue life of the bridge is in theory infinite. All calculations and analysis was done using the structural analysis program Staad.Pro 2004. In this report the methods of modeling and analysis have been laid out so hopefully, they will be useful for individuals who wish to study stress ranges in other bridges. This study has proven insightful and very helpful as that it covered an area of immense personal interest and taught the method and application of computer simulation using the Staad program.
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Acknowledgements •
Prof. Dennis Mertz
•
Dr. Michael Chajes and Diane Kukich
•
Doug Finney of DelDot
•
Elliot Fink
•
Mark Guzda
•
Tim Stuffle
•
Michelle Bensi This material is based on work supported by the National Science Foundation under Grant No. EEC 0139017, “Research Experiences for Undergraduates in Bridge Engineering,” at the University of Delaware.
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References •
Barsom, John M. & Rolfe, Stanley T. Fracture and Fatigue Control in Structures. 3rd ed. West Conshohocken: ASTM, 1999.
•
Fisher, John W. "Bridge Fatigue Guide Design and Details." American Institute of Steel Construction, New York, N.Y., 1977 p. 17-20.
•
Hertzberg, Richard W. Deformation and Fracture Mechanics of Engineering Materials. 4th ed. Hoboken: John Wiley and Sons, Inc, 1996.
•
http://www.oregon.gov/ODOT/TD/TP_RES/docs/Reports/FatigueCrack.pdf
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"LRFD Bridge Design Specifications." AASHTO Customary U.S. Units 2nd Edition, 1998 (1998): 6.61-6.62.
•
Mertz, Dennis R. "Bridge Fatigue Myths." Bridge Crossings. 4 Febuary 1997. AISC. 10 Aug. 2005 .
•
Moses, F., C.G. Schilling, and K.S. Raju. "Fatigue Evaluation Procedures for Steel Bridges." National Cooperative Highway Research Program Report November 1987: 11-16, 70-74, 74-77, 59-67.
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Appendix A Fatigue Detail Pictures and Ilustrations
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Appendix B Case Loadings & Deck Stress Distributions
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Load Case 1
30
Load Case 2
31
Load Case 3
32
Load Case 4
33
Load Case 5
34
Load Case 6
35
Load Case 7
36
Load Case 8
37
Load Case 9
38
Load Case 10
39
Appendix C Delaware Department of Transportation Plans For Delaware Bridge #771
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Overpass at Shipley Road Plan and Elevation
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Overpass at Shipley Road N. B. L. Framing Plan
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Overpass at Shipley Road N. B. L. Deck and Approach Slabs Plan and Bar Schedule
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Overpass at Shipley Road N. B. L. and S. B. L. Sections and Details
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Appendix D Procedure for Defining and Generating Moving Truck Loads Using Staad. Pro 2004
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Load Definition The first step in applying a moving truck load to a model is to define the load. Figure1- D shows how to define the loadings option by selecting the command tab on the main toolbar. From there, highlight the definitions option and ultimately select the vehicle option.
Fig 1-D How to define a vehicle load
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After the load is defined as a vehicle, the actual weight of the load needs to be entered into the program. This can be done in one of two ways; the axle spacing and weight of the vehicle can be entered manually, or the vehicle can be selected from a number of predefined trucks in Staad. Fortunately, the HS – 15 truck is already defined and can be selected from the AASHTO Spec menu seen in Figure 2 -D
Fig 2-D Menu of pre-defined AASHTO trucks
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Moving Load Generation Defining the load as a vehicle and assigning the properties of an HS-15 truck are necessary steps, but in order to simulate a moving truck the load must be placed at a number of positions on the bridge. In order to do this a moving load must be generated using Staad. From the Commands tab select the loading option and highlight the moving load generation option. From there a pop-up box will appear and want to know the number of load generations desired. For the study a 10 generated loads were used. After the number of truck loads generated has been determined a box will show on the right side of the screen. Within this box highlight the load case with the generated loads. Select the add button at the bottom of the box and this will cause a pop-up menu to appear. Inside the initial position of the vehicle can be determined in the x, y, and z directions. In addition to the initial position, the spacing interval can be entered for the distance between each generated load in the x, y, and z directions. Finally, an outline of the load will become visible on the applied structure. Figures 3-D through 6-D will illustrate the outlined steps.
Fig 3-D Selection of the moving load generation option
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Fig 4-D Selection of number of generated loads
49
Fig 5-D Determination of initial position and intervals of generated loads
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Final Generated load
Fig 6-D Final generated applied moving truck load
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Appendix E Stress Range Graphs for Transverse and Longitudinal Welds
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Transverse Welds Northern Side
Max Stress = 2.15 KSI in Beam 99
53
Southern Side
Max Stress = 1.2 KSI in Beam 103
54
Longitudinal Welds Girder One
Girder One Stress Range 2500 Load Case 1
2000
Load Case 2 Load Case 3
S tr e s s (p s i )
1500
Load Case 4 Load Case 5
1000
Load Case 6 Load Case 7
500
Load Case 8 Load Case 9
0
Load Case 10
-500 0
10
20
30 Span (ft)
Max Stress = 2.2 KSI
55
40
50
Girder 2
Girder Two Stress Range 3500 3000
Load Case 1
2500
Load Case 2 Load Case 3
S tr e s s (p s i )
2000
Load Case 4
1500
Load Case 5
1000
Load Case 6 Load Case 7
500
Load Case 8
0
Load Case 9 Load Case 10
-500 -1000 0
10
20
30 Span (ft)
Max Stress = 3.2 KSI
56
40
50
Girder 3
Girder Three Stress Range 1600
S tr e s s (p s i )
1400
Load Case 1
1200
Load Case 2
1000
Load Case 3
800
Load Case 4 Load Case 5
600
Load Case 6
400
Load Case 7
200
Load Case 8
0
Load Case 9 Load Case 10
-200 -400 0
10
20
30 Span (ft)
Max Stress = 1.53 KSI
57
40
50
Girder 4
Girder Four Stress Range 400 Load Case 1
300
Load Case 2 Load Case 3
S r e s s (p s i )
200
Load Case 4 Load Case 5
100
Load Case 6 Load Case 7
0 0
10
20
30
-100
40
50
Load Case 8 Load Case 9 Load Case 10
-200 Span (ft)
Max Stress = .36 KSI
58
Girder 5
Girder Five Stress Range 700 600
Load Case 1
500
Load Case 2 Load Case 3
S tr e s s (p s i )
400
Load Case 4
300
Load Case 5
200
Load Case 6 Load Case 7
100
Load Case 8
0
Load Case 9 Load Case 10
-100 -200 0
10
20
30 Span (ft)
Max Stress = .6 KSI
59
40
50
Girder 6
Girder Six Stress Range 150 Load Case 1 100
Load Case 2
S tr e s s (p s i )
Load Case 3 Load Case 4
50
Load Case 5 Load Case 6 0
Load Case 7 Load Case 8 Load Case 9
-50
Load Case 10 -100 0
10
20
30 Span (ft)
Max Stress = .11 KSI
60
40
50
