Failure Analysis of a Steel Slab-On-Girder Bridge Weidner Report

7/31/2019 Failure Analysis of a Steel Slab-On-Girder Bridge Weidner Report

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Failure Analysis of a Steel Slab-On-Girder Bridge

Kris Weidner

University of Delaware

Advisors: Dr. Michael ChajesDr. Jennifer Righman

Graduate Advisor: Justin Ross


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Table of Contents

Abstract ............................................................................................................................... 4

Chapter 1: Introduction ...................................................................................................... 5

1.1 Problem..................................................................................................................... 5

1.2 Why it is important ................................................................................................... 5

1.3 Approach to Solving ................................................................................................. 6

Chapter 2: Background ...................................................................................................... 6

2.1 Past Destructive Tests............................................................................................... 6

2.2 Bridge 11................................................................................................................... 7

2.3 Details of Bridge 7R ................................................................................................. 8

Chapter 3: Planned Test ................................................................................................... 10

Chapter 4: Previous Diagnostic Test................................................................................ 12

Chapter 5: Model and Comparisons to Diagnostic Test .................................................. 13

5.1 Creation of Model ................................................................................................... 13

5.2 Comparisons to Diagnostic Test ............................................................................. 17

5.3 Spreader Beam Test ................................................................................................ 195.4 Plastic Deformation and Load Redistribution ........................................................ 22

5.5 Ultimate Load Test - STAAD................................................................................. 23

Chapter 6: Results and Conclusion .................................................................................. 27

Acknowledgments............................................................................................................. 29

References......................................................................................................................... 30

Appendix........................................................................................................................... 31


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List of Figures

Figure 1: Bridge 7R side view9

Figure 2: HS20 Truck dimensions.10

Figure 3: Spreader Beam measurements (also in Appendix A)........11

Figure 4: Pass 1 (top left), Pass 2 (bottom middle),

Pass 3 (top right)12

Figure 5: Diagnostic Test Gauge Placement.13

Figure 6: Wire frame model of the S9-S12 Girder on Bridge 7R................14

Figure 7: Full Scale Bridge Model (Top and Right Side View)...15

Figure 8: Full Scale Bridge Model Pass 3 Diagnostic Test

Simulation.16

Figure 9: Comparisons between Diagnostic Test pass

and STAAD simulated pass 3...............................................................................18

Figure 10: Spreader Beam by itself..................................................................................20

Figure 11: Spreader beam and deck deflection comparisons.......21

Figure 12: Complete Bridge with spreader beam.21

Figure 13: Variations in bending stresses due to increasing

moment about x-axis. (McCormac, 2003).............................................................22

Figure 14: A Plastic Hinge (McCormac, 2003)23

Figure 15: Single beam example of plastic hinge creation.......25

Figure 16: Layout of bridge showing movement of hinges as

they formed...26


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1.3 Approach to Solving

Destructive tests must be extremely accurate and proper data must be gathered during the

test. Since there is only one chance to run the test much preparation is needed. As a

result of the recent destructive test on Bridge 11 we have learned many new things about

what should and should not be done. All of that knowledge has been taken into account

in the planning for the destructive test of Bridge 7R. This project focused on using a

three dimensional numerical computer model to help predict the behavior of the bridge,

and using the prediction, refine the test plan to ensure a successful test... The final test

can be extremely dangerous if not carried out properly so the loading process designed by

HNTB has been tested with the STAAD model. The model will indicate where the

girders will form plastic hinges, and this will help determine where strain gauges should

be concentrated. The model will also be used to refine the spreader beam design that has

been proposed to load the bridge. Finally, the results of this study will help increase the

knowledge of destructive tests and aid in the process of developing protocols for them.

Chapter 2: Background

2.1 Past Destructive Tests

Even though destructive tests can be very valuable to our knowledge of bridges, they do

not occur very often. It is rare that people are given the opportunity to destructively test a

bridge that was designed for a fifty to a hundred year lifespan. There were only a few

prior destructive tests to Bridge 11 that previous research could find here at Delaware.

These are the Stoney Creek Bridge in London, Ontario, Canada. Two more bridges in


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Ohio, one having an eight-panel Pratt Through Truss and the other having a Camelback

Through Truss. The third test that was found was reinforced concrete slab-bridge in

Ohio, and the fourth was again in Ohio, but was a pre-stressed box beam bridge. The

next two bridge types found for destructive testing were out of the country. These were

full-scale destructive test of a precast segmental box girder bridge held in Bangkok,

Thailand, and the next used fiber optic monitoring during the destructive test conducted

by the Norwegian University for Science and Technology in Trondheim, Norway. Lastly

a curved steel I-girder bridge was initiated by the federal highway administration

(FHWA) and supported by HDR Engineering. This was performed at Turner-Fairbanks

Research Center. To find more detailed information about these tests, see the thesis

written by Peter Quinn (Quinn, 2005).

This is evidence that not many destructive tests have been performed and that more

bridges have to be tested to completely understand a bridge system and how it works.

2.2 Bridge 11

Even though destructive testing of bridges is rare, the University of Delaware has had the

opportunity to test one in the past and will have more to test in the future. Bridge 11 was

a three-span continuous steel girder bridge with a composite concrete deck. This bridge

was 50 years old and had a five girder system. Each girder was Grade 36 W36x150 steel.

This bridge was also on a 56 degree skew to the roadway and served as an exit ramp for

Interstate 295 through Delaware. For this destructive test the bridge was wired with a

total of 102 strain gauges. Having this large amount of gauges made sorting through data

difficult and lengthy. The load was applied by adding asphalt millings to the bridge span.

At the end of the testing the total load on the mid span consisted of 14 barriers, 8


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truckloads of material, and 200 scoops of millings from the loader adding up to a total of

8,896 kN or about 2000 kips. This way of testing was not very accurate and caused

numerous problems along the way, such as cutting the bottom flange of the first girder so

yielding could start to occur. This was caused by a lack of planning. There was no pre-

test model and there was also a limited amount of load to be had, so when the loading did

not cause the bridge to yield they had to improvise.

2.3 Details of Bridge 7R

Now that Bridge 11s testing is complete we have learned a lot about what should and

should not be done during the destructive testing of Bridge 7R. Understanding now how

difficult testing a bridge to failure can be, pre-test models have been created. One model

has been created in STAAD Pro.2003 and another Finite Element Analysis model using

ABAQUS. This will help with gauge placement throughout the bridge so 102 strain

gauges will not be necessary. A great deal has also been learned about the loading

process of a bridge. Having a limited amount of load that could be applied to the bridgedid not work in the case of Bridge 11 so the opened engineering contractor to the

Delaware River and Bay Authority, HNTB, has proposed a design for a new jacking

system. HNTB and the University of Delaware are working together on this project to

make sure it runs smoothly. Instead of adding load to the top of the bridge deck, HNTB

has proposed that a jacking system be applied from the bottom of the bridge pulling down

from the deck. Much preparation is going into the destructive test of Bridge 7R due to

the lack of preparation that was necessary on Bridge 11.

Bridge 7R is a steel slab-on-girder bridge with a composite concrete deck. The bridge

was built in 1961 and is an exit ramp on I-295 running north through Delaware. It is still


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Mechanical Ground Anchors, Model Stingray SR-3. The jacking system will start with

each jack registering 4 kips. The original plans say that the jacks will increase the load

by 4 kips each cycle for 13 cycles, but further analysis has shown that the bridge will

withstand at closer to 23 cycles of loading. The jacking system will therefore add load

for 23 cycles or until the testing apparatus or bridge fails first. As a result of the under

designing of the jacking system, it had to be tested with the models to make sure the

spreader beams would not fail before the system reached the ultimate load. A test was

run using STAAD on the full scale model which will be explained later in detail. This

system should prove to be much more effective and accurate than the loading system on

Bridge 11. This loading is slow and continuous and not large sums of asphalt millings

being poured onto the bridge at once. There is also a lot more control and safety in this

jacking system since we can stop and release the loading whenever necessary.

(See Appendix A for plans of the spreader beam designed by HNTB)

Figure 3: Spreader Beam measurements (also in Appendix A)


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Chapter 4: Previous Diagnostic Test

A diagnostic test was run on Bridge 7R in the fall of 2005. This test involved shutting

down the exit ramp for the amount of time to run a fully loaded HS20 truck down the

ramp at three different positions. The truck ran from west to east each time. The first run

the truck was on the left side nearest to girder number 1, the second time the truck ran

down the middle, and the third time the truck ran down the right side nearest girder 4.

Figure 4: Pass 1 (top left), Pass 2 (bottom middle), Pass 3 (top right)

There were in total eight strain transducers and two potentiometers. Strain transducers

measure the amount of strain that is being applied at that point and the potentiometer

measures the displacement at that point. The objective of this diagnostic test was to see

how service level truck loads were redistributed throughout the bridge. The diagnostic

test results can be used to validate a variety of computer models of the bridge including

the finite element analysis model that the graduate student Justin Ross is working on, and

also the STAAD model used herein. The data from the diagnostic test will allow us to

make sure our results are acceptable.


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Figure 5: Diagnostic Test Gauge Placement

Chapter 5: Model and Comparisons to Diagnostic Test

5.1 Creation of Model

The model for this research project was created using STAAD Pro.2003. STAAD stands

for structural analysis and design and can do just that. It is a program made specifically

for designing and analyzing structures all at the click of a mouse. To begin designing this

model I had to first become familiar with STAAD since I have never used it before. The

first model that was created was a single model for each girder on the bridge. The

measurements for each girder had to be specifically defined in the program since they are

not the same and are not usual measurements. The beams also needed a portion of the

concrete deck applied to them so the analysis would involve the stiffness of the decking.

Bridge 7R is a steel girder bridge with a composite concrete deck so a process had to be


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formed to attach the deck rigidly to the four girders. Nodes were created to attach the

beams and the deck using cylindrical steel bars.

Figure 6: Wire frame model of the S9-S12 Girder on Bridge 7R (More available 3D bridge renderings in Appendix B)

The cylindrical steel bars went from the centroid of the Girder to the centroid of the

concrete deck because the way STAAD works the measurements are made from the

center out. This design worked very well so it was later incorporated into the full scale

bridge. After applying load to my structure results were gathered and it was time to

create the full scale bridge model. Once I learned STAAD better, making complex

models such as this became increasingly easier.

Cylindrical steel bars which act asthe rigid link between the steelgirder and concrete deck.


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Figure 7: Full Scale Bridge Model 3D Rendering (Top and Right Side View)

(More available 3D bridge renderings available in the Appendix B)

The full scale model was started in the same basic way as the individual beams, but the

skew of the bridge now had to be taken into account. Hand calculations were performed

to measure the distance the nodes had to be away from the axis. After the skew was

drawn the main girder beams were put into place making sure that there were enough

nodes to later rigidly attach the concrete deck to the beams. While in the process of

adding the deck I made sure that there were also nodes in place to attach the spreader

beam on top of the deck. The spreader beam is going to be used to load the bridge to

failure in the spring of 2007. HNTB made designs that needed to be tested later with my

model. A series of plates were used to form the composite deck and after everything was

together each plate and beam had to be assigned properties. As a result of the main

girders having different dimensions that are not well known the properties were

individually defined in the program. Each plate was also defined at eight inches thick

throughout the entire deck. The rigid links that held the concrete deck to the girders were


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Figure 9: Comparisons between the Diagnostic Test pass 3 and STAAD simulated pass 3.

(See Appendix C for Graph Comparisons)

Pass 3 (Right Side)

0

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m i c r o s

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348

STAAD (simulated Pass 3)

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static load

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5.3 Spreader Beam Test

HNTB has designed the loading process for when the bridge will be loaded to failure.

This test will consist of a series of jacks, anchored below the bridge, which will pull

down on the bridge. These jacks will each pull with a force that incrementally rises to

create a higher and higher amount of load. The loading that will be applied will simulate

a fully loaded HS20 truck and as the loading increases it simulates more that one of those

trucks at the exact spot. The idea behind this is to figure out how many trucks it would

take to load the bridge until failure. The spreader beam, which is the beam that will

support the jacks on the concrete deck, was only designed to hold about 13 truck loads.

13 truck loads is about 936 kips and each jack will be pulling down to simulate a load of

52 kips. Later we estimated that the bridge will probably need to be loaded to about 23

truck loads or 1,656 kips. That means each jack will be pulling down to simulate a load

of 92 kips (more than the design load). Due to the higher load, we need to also ensure

that the spreader beam can handle that kind of force without deflecting into the concrete

deck. There are only two inches of clearance between the bottom flange of the spreader beam and the top of the concrete deck so the whole system had to be tested in STAAD.

The spreader beam is a MC12x50 type beam and it has a 1 5/8 in. gap between the

channels. This beam is to be placed directly on top the concrete deck on the same part of

the bridge where the truck took pass 3 in the diagnostic test. This will allow the gauges

to pick up the strains as the bridge reaches its inelastic state and it will detect how the

bridge distributes the load from one girder to the next as that occurs. To see the complete

plans of HNTB see Appendix A. In order to create a spreader beam full bridge system a

simpler model of the spreader beam was made. First, the dimensions of the beam were

received off of the HNTB plans and then a model was designed based on those results.


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The first model that was designed was a simple model of just the spreader beam. The

spreader beam in this model sat upon the steel plates that acted as the wheels of the HS20

truck.

Figure 10: Spreader Beam by itself

After designing the beam to the proper dimensions and running a few simple load tests to

see how it would perform the spreader beam was incorporated into the full scale model.

The spreader beam had to act as if it was sitting directly on top of the concrete deck. This

was achieved by using similar rigid links between the girders and the concrete deck.

These rigid links connected the center of each steel plate, which was supporting the

spreader beam, and a node that was positioned directly below the center of the plate.

This allowed the beam to act as if it was a part of the whole bridge system. Once the

bridge system was complete and all the properties of the bridge were assigned, each jack

position on the spreader beam was loaded appropriately. The spreader beam on the

bridge deck was loaded incrementally, starting with a single truck load and increasing by

ten truck loads until it reached forty truck loads. By increasing the load incrementally

STAAD could more easily show how the bridge and spreader beam were behaving as a

system as the load was being applied, much like the actual load test will be performed.


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Figure 11: Complete Bridge with spreader beam

Now that the loads have been applied to the complete bridge with the spreader beam

attached to the deck, the test can be run and the results can be processed.

Figure 12: Spreader beam and deck deflection comparisons.

(See more data on deck deflections see Appendix D)

Spreader Beam and Deck Deflection Comparison

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

0 5 10 15 20 25 30 35 40 45

Number of "Trucks" loaded

D e

f l e c

t i o n

( i n c

h e s

)

Spreader Beam Deflection Deck Deflection

The spreader beamdoes not hit the deckuntil 30 to 31 truckloads.

23 kips is thepredicted loadto reachplastic failurefor Bridge 7R

Both spreader beamsattached to the concretedeck with rigid links.


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5.4 Plastic Deformation and Load Redistribution

In the next section to better understand the ultimate load calculations using STAAD a

brief background will explain plastic deformation and load redistribution. Plastic

deformation is the change in shape due to an applied force. (McCormac, 2003) Unlike

elastic deformation plastic deformation is not reversible. However, an object has to go

through elastic deformation before it can approach the plastic state. As an example

consider a steel beam. As moment is applied to the beam, the stress will be distributed

throughout the beam until it reaches its yielding point. If the beam continues to be

stressed passed the yielding point the part of the beam which is already yielding, it will

remain in that state while the rest of the beam nearing the neutral axis will take on the

remaining stress. This occurs until the entire beam is being used in taking the stress that

is being applied. (McCormac, 2003)

Note that the variation of strain from the neutral axis to the outer fibers

remains linear for all of these cases. When the stress distribution has

reached this stage, a plastic hinge is said to have formed because noadditional moment can be resisted at the section. Any additional moment

applied at the section will cause the beam to rotate with little increase in

stress. (McCormac, 2003)

Figure 13: Variations in bending stresses due to increasing moment about x-axis.

(McCormac, 2003)


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When the beam is in a complete plastic state a plastic hinge will form at the area where

the moment is being applied. The area of this hinge can no longer take any moment,

therefore the moment will be distributed along the beam depending on the type of

structure it is.

Figure 14: A Plastic Hinge (McCormac, 2003)

In the past plastic theory has proven to distribute stresses after certain points in a

structure have reached their yield stress. In a more complex system of beams after a

plastic hinge has occurred at one point, the loads will be redistributed across the rest of

the structure and they will take the additional stress. By loading Bridge 7R to failure we

will be able to witness plastic hinges occurring at different points. Then we will be able

to see how the loads are being redistributed across the deck and other girders to support

the load. This load redistribution will allow the bridge to withstand much higher forces

than it was designed to uphold.

5.5 Ultimate Load Test - STAAD

The final part of this research project is to see how Bridge 7R will behave plastically. To

test the full bridge model, including the spreader beam, it will be tested by following a

very methodical process. In order to learn this process properly a test was first done on a

120 foot beam with the same properties as girders S9 and S12 on the bridge. There was


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a load applied 1/3 or 40 feet from the left side of the model. I knew from examples in the

textbook (McCormac, 2003) that plastic hinges would occur at three places, but I did not

know the order that they would occur. Since STAAD is an elastic program by design it

was not straight forward as to how it would be relevant that the beam became plastic. As

a result calculations that were done by the graduate student, Justin Ross, and were

checked by me were used to find the plastic moment of the girder S9-S12. Since I knew

the plastic moment of the beam I could now use a systematic approach to the model that I

made to understand when the yielding would begin. First loading was applied to the

bridge, and a test was run. After I saw the results I could figure out how much more

loading was needed for the beam at the point to reach its plastic state. After finding the

proper amount of load the test was run again with that load and the results were checked

again. From this the moments that occurred at the other two positions could be seen just

like the text said. Then the moments were released at the point where the beam was

inelastic and the test was run again. Since the beam was loaded till it reached the plastic

limit at a point the beam will continuously hold that amount of load, but can no longer

take any more moments. Therefore the next moment to match is the difference between

the previous maximum moment and the next highest moment. This will make the model

act as if there was never a new test run. This process will continue until the three hinges

are formed. The first hinge is on the left support, the second where the load was applied,

and the third on the second support. These results are only accurate for this scenario, but

give a good background for the final test. Also a graph was made showing the deflection

versus the load in kips. This graph shows the relationship of how the load bulk of the

load and deflection occurs initially, but some of the load still is being redistributed

throughout the beam even when the third hinge is formed.


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Figure 15: Single beam example of plastic hinge creation.

(To see the complete example of this test see Appendix C.)

Now that a process has been developed for simulating plastic hinges using STAAD, this

process had to be applied to the full scale model of Bridge 7R. The complexity of the full

bridge is far greater than a single beam so now there are four separate girders that have to

be taken into account. This system of loading and releasing moments can be carried out

by these following steps.

1. First solve the plastic moment capacity in each beam.

2. Then load the bridge with an arbitrary amount, so the amount of load needed to

cause the beam to reach its plastic moment can be determined.

3. Once the specific load is known, analyze the model to see what the second highest

moment is.

Mz = 120606.04 kip-in= 10050.5 kip-ft

Mz = -81480.328 kip-in= -6790.027 kip-ft

Mz = -61917.477 kip-in= -5159.78975 kip-ftPp = -570.386 kips


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4. When that is recorded you can release the moments at the position of the highest

moment and re-analyze the bridge.

5. This will know allow you to look at the second highest moment the same way you

did to the previous moment since the first beam can no longer take a moment at

that point.

This process shall be repeated until all of the reasonable plastic hinges have been formed.

This model went through the process until there was a plastic hinge in each girder. This

model and process showed very accurately how the load would be distributed

transversely across the bridge as plastic hinges would form.

(See Appendix G for the data and figures explained in the previous process.)

Figure 16: Layout of bridge showing movement of hinges as they formed.

#1#2

#3

#4

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aa mm oo uu nn ttss oo f f lloo aa dd aa r r ee nn ee ee dd ee dd ttoo f f oo r r mm hh iinn gg ee ss aa tt gg iir r dd ee r r ss ## 11 aa nn dd ## 22 ..

Hinge

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Hinge 3

Hinge Movement towards support


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Chapter 6: Results and Conclusion

The STAAD model is extremely accurate in the elastic region especially since STAAD is

designed to handle elastic modeling, but with the procedure that was discussed in Chapter

5.5 even simple modeling in the inelastic region is possible.

The first important test that was run using the STAAD model of Bridge 7R was to decide

whether the spreader beam under the ultimate load would deflect further than the bridge

deck causing them to touch. After analysis it was conclude that the spreader beam will

deflect into the deck of the bridge at about 30 to 31 truck loads which is over the total

amount of loading that that bridge will support. The spreader beams original design will

still be sufficient despite being under designed by ten truck loads.

Being able to see how the Bridge 7R will perform under loads that cause it to plastically

deform was the main purpose of this model. This includes the positions of plastic hinges

as they travel transversely across the bridge. During the analysis that was performed and

explained in Chapter 5.5 some interesting results were discovered. It turns out that as the

plastic hinges were forming, they were working their way towards the eastern support on

girder #1. This was causing enormous amounts of load to be applied in order to create

plastic hinges on girder #s 1 and 2. Since most of the load is coming from the section of

the spreader beam that simulates the back axels of the HS20 truck, the load has a much

stronger tendency to work its way towards the support (17.56 feet away from the rear of

the spreader beam) rather than towards girder #1, which is about 44.33 feet away. The

shorter distance is the reason why the plastic hinges want form toward the support.


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One way to fix this problem is to simply move the position of the spreader beam so the

rear axel is further away from the support and has to travel a further distance to get to it

than the position of the final plastic hinge. The spreader beam could also just be rotated

180 degrees so the rear axel is on the other side of the bridge, which due to the skew

would naturally keep it further away from a support.

Understanding how Bridge 7R will plastically deform and how the loads will be

redistributed before the final test will help us design a more effective test program.

Results from a successful test will allow for us to better understand the actual capacity

that a bridge can handle and can help bridge designers to design with less material, but a

longer lifespan, which will greatly keep down the cost. Based on the destructive test

results it is possible to show that certain bridges currently being taken out of commission

may still be strong enough to be used for a few more years. This will all be possible with

a better understand of how a bridge distributes its load during plastic deformation, and

the results may enable bridge owners to save money on unnecessary bridge replacement,

and instead use the money for other transportation needs.


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Acknowledgments

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.

Advisors: Professor Chajes

Jennifer Righman

Graduate Advisor: Justin Ross

Graduate Student: Geoff Burrell

REU Students: especially Michelle Banister and Katie Wehrum


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References

McCormac, Jack C., Nelson, James K. Jr. 2003, Structural Steel Design LRFD Method

Third Edition, Pearson Education, Inc. Upper Saddle River, NJ 07458: 215-231

Quinn, Peter L. 2005, Understanding Steel Bridge Behavior through Destructive Testing,

Thesis (M.C.E.) - University of Delaware, 2005: 5-16

Ross, J., Righman, J., Chajes, M., Mertz, D. 2006, Evaluating ultimate bridge capacity

through destructive testing of decommissioned bridges.


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Appendix

Appendix A: Scaled Bridge Drawing and plans for spreader beam designed by HNTB

Appendix B: 3D view of Bridge 7R from numerous angles

Appendix C: Graphs Showing Data Comparisons between Diagnostic Test and STAAD

Model. This involves the data collected from strain gauges in the on the bottom

flange of Beams 1, 2, 3, and 4. They would be gauges 317, 299, 338, and 348.

Appendix D: Graphs and Data showing when the spreader beam will hit the deck due to

deformation of the deck versus the spreader beam.

Appendix E: Pictures and a Table showing test in STAAD how to add plastic hinges to a

beam in order to display the plastic deformation and load redistribution using

STAAD.

Appendix F: Data and Graphs showing the process explained in chapter 5.5. This

graphically explains how to model plastic behavior in STAAD.


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Appendix A


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Appendix A


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Appendix B

Girder S9-S12

Girder S10-S11


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Appendix B

Wire Frame view of Girder S9-S12.

Head on view of Bridge 7R.


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Appendix B

Full Bridge View including Spreader Beam.

Spreader Beam


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Appendix B

Underside of Bridge 7R, STAAD Model, 3D rendered view.


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Appendix B

Loading spreader beam on Bridge 7R.

Scaled Load Displacement of Bridge 7R with Spreader Beam.


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Appendix B

Deck stresses due to simulated truck load applied to spreader beam.


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Appendix C

Pass 1 (Left Side)

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Abaqus Pass 1

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Appendix C

Pass 2 (Center)

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Appendix C

Pass 3 (Right Side)

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static load

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Abaqus Pass 3

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Appendix D

Deck and Spreader Beam data for deflections when increasing number of trucks is

applied.


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Appendix E

Mp for S9-S12 = 10050.5 kip-ftRun 1

Vertical Y = -4.448 in

Run 2


Mz = 120606.04 kip-in= 10050.5 kip-ft

Mz = -81480.328 kip-in= -6790.027 kip-ft

Mz = -61917.477 kip-in= -5159.78975 kip-ftPp = -570.386 kips

Mz = -39127.094 kip-in= -3260.5911 kip-ft

Mz = -33146.723 kip-in= -2762.2269 kip-ftPp = -156.6 kip


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Appendix E

Run 3


Plastic Deformation of S9-S12 Girder

0

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300

400

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600

700

800

0 1 2 3 4 5 6 7 8 9

Deflection

L o a

d ( k i p s

)Run 1

Run 2

Run 3

Graph showing the deflection versus the load.

Mz = -5980.368 kip-in= -498.364 kip-ftPp = -6.22955 kip

Third Plastic Hingewill go here.


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Appendix F

Full Scale Bridge Model with Spreader Beam to Plastic Failure

S9-S12 Mp = 10050.5 kip-ft S10-S11 Mp = 8610.98 kip-ft

Run 1Load Total = 1386.025829 kips About 19 truck LoadsLoad Individual = 77.00143492 kipsBeam: 569

Node: 107

Spreader Vertical Y = -8.270 in

Deck Vertical Y = -7.016 in

Run 2Load Total = 51.71963017 kips About 20 truck LoadsLoad Individual = 2.873312787 kipsBeam: 71

Node: 82

Spreader Vertical Y = -.582 inDeck Vertical Y = -.479 in

Mz = 120605.96 kip-in= 10050.5 kip-ft

Mz = -6374.726 kip-in= -531.2271667 kip-ft


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Appendix F

Run 3Load Total = 804.4728143 About 31 Truck LoadsLoad Individual = 44.69293413Beam: 550

Node: 66

Spreader Vertical Y: -16.160 inDeck Vertical Y: -12.786 in

Run 4Load Total: 1470.859909 kips About 51 Truck LoadsLoad Individual: 81.71443939 kipsBeam: 540

Node: 44

Spreader Vertical Y: -41.659 in.Deck Vertical Y: -33.225 in.

Mz = 100161.15 kip-in= 8346.7625 kip-ft

Mz = -80475.742 kip-in= 6706.311833 kip-ft


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Appendix F

Order that plastic hinges appeared on the Girders.

Run 1

Run 2

Run 3

Run 4

Failure Analysis of a Steel Slab-On-Girder Bridge Weidner Report

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