SUMMARIES OF ANALYSES OF CASE- STUDY BRIDGES 4 The...

NCHRP Project 12-87a

B-1

APPENDIX B 1

SUMMARIES OF ANALYSES OF CASE-2

STUDY BRIDGES 3

The analyses performed on case-study bridges to develop the finite element analysis (FEA) methodology 4 and calculate dynamic amplification factors are summarized in the current appendix. Each of the case-5 study bridge finite element models was (1) benchmarked against available experimental data, (2) used to 6 calculate dynamic amplification factors, and (3) evaluated for redundancy in accordance to the developed 7 analysis methodology. The contents in the current appendix are organized as follows: 8

• Section B.1 summarizes the analysis carried out for the Neville Island Bridge. 9 • Section B.2 summarizes the analysis carried out for the Hoan Bridge. 10 • Section B.3 summarizes the analysis carried out for the University of Texas Twin Tub Girder 11

Bridge. 12 • Section B.4 summarizes the analysis carried out for the Milton Madison Bridge. 13 • Section B.5 summarizes the analysis carried out for the White River Bridge. 14 • Section B.6 summarizes the analysis carried out for the Dan Ryan Expressway Transit Structure. 15


B-2

B.1 Summary of Analysis Performed for the Neville Island Bridge 16

The portion of the Neville Island Bridge that has been analyzed is the northbound structure over the 17 backchannel of the Ohio River. This structure is a welded two-girder system continuous over three spans, 18 with 215 feet end spans and 350 feet center span. In 1976, a large crack was detected in the fascia girder 19 (girder G4) in the middle of the center span. The cracks originated at a defective electro-slag weld an 20 extended throughout the cross section, arresting before reaching the top flange. Figure B-1 shows the 21 location where the crack was detected. 22

23

24 Figure B-1. Geometry of the Neville Island Bridge and fracture location. 25

Very small deflection (about five inches at the location of the fracture) was observed after the crack 26 detection, and the structure carried traffic loads in the faulted condition. J. W. Fisher et al. (1980) 27 investigated the cause of the fracture and describes the conducted repair operations. Results from field tests 28 reported in J. W. Fisher et al. (1980) were used to benchmark the constructed finite element model [1]. 29 Field testing was performed and included strains measured at various locations on the girders recorded as 30 the fractured girder was jacked back together. The measured jacking loads were applied to the failed girder 31 with the simulated fracture and the result obtained from the model were compared to the available field 32 data. 33

B.1.1 Finite Element Model Features 34

A 3D finite element model was constructed in accordance with the proposed FEA methodology for 35 system analysis. The geometry and nominal material properties input in the analysis were as described in 36 the design plans. The model was composed of: 37

• Two parallel girders modeled with shell elements. The girders were attached to connector elements 38 modeling pier flexibility. 39

• A system of truss floor beams and lateral braces modeled with beam elements. The welded plate 40 floor beams were modeled with shell elements. The connections among stringers, floor beams and 41 girder were modeled with a mesh tie constraint. The nominal capacity of the connections were 42 determined to be larger than the individual member capacities; therefore, connection failure need 43 not be modeled for the Neville Island Bridge. 44

• Three stringers modeled with shell elements. The connection between the stringers and the floor 45 beams was modeled with a mesh tie constraint. 46

• A slab in which concrete was modeled with solid elements and rebar with embedded truss element. 47 Contact interaction that considers “hard” normal and frictional tangential behavior was specified 48 between the slab and the steelwork. 49

The bridge was analyzed using the procedures developed to compute dynamic amplification factors for 50 redundancy evaluation (DAR) and evaluate the structure for the Redundancy I and Redundancy II loading 51 combinations. Figure B-2 shows a detail of the geometry of the structure. 52

53


B-3

54 Figure B-2. Detail of the geometry of the Neville Island Bridge finite element model: concrete slab 55 (grey), rebar (black), girders (blue), floor beams (red), stringers (magenta), lateral bracing (green)). 56

B.1.2 Benchmarking 57

An analysis was carried out to determine whether the finite element model captured the behavior 58 exhibited by the portion of interest of the Neville Island Bridge. The stiffness of the elements in the web 59 and bottom flange of Girder G4 was relaxed at the location of the fracture while the structure was under 60 dead load only in order to replicate the state of the structure before its repair. A deflection of 5.9 inches 61 was calculated in the finite element analysis, which is similar the deflection of 5 inches observed by J. W. 62 Fisher et al. (1980) (this deflection was estimated and not directly measured) [1]. 63

Next, the jacking operation performed in the field to close the crack before installing a bolted splice was 64 replicated in the finite element analysis. Strain gage measurements described in J. W. Fisher et al. (1980) 65 were used to benchmark the constructed finite element model. The data consisted of closing force-closing 66 displacement data, and changes in stress distributions after the jacking operation was completed. Figure 67 B-3 shows the location of the sections at which the stress distributions were measured [1]. 68

69

70 Figure B-3. Location of sections where stress data is available form J. W. Fisher et al. (1980). 71

J. W. Fisher et al. (1980) reported that the structure behaved compositely although it was designed as 72 non-composite. Two approaches were used to model the contact tangential behavior, a rough contact model 73 that does not allow slip between points in contact and a frictional contact model. Both approaches to the 74 tangential contact behavior resulted in good correlation with the data reported in J. W. Fisher et al. (1980), 75 showing that the structure behaved compositely while in service [1]. This is shown in Figure B-4 for the 76 closing force-closing displacement data, and in Figure B-5, Figure B-6 and Figure B-7 for the changes in 77 stress distributions. 78


B-4

As can be seen, the model yielded very good correlation with observed deflections and field measured 79 strains. Based on these data and the overall response of the finite element model matching overall behavior 80 of the bridge in the faulted state, the approach for modeling the non-composite slab and the structural steel 81 was deemed reasonable. 82

83

84 Figure B-4. Comparison of closing force versus closing displacement relations. 85

86 Figure B-5. Comparison of longitudinal normal stress change during repair operation at section 1 87

in girder G3. Closing force of 1674 kips. 88

0

500

1000

1500

2000

0 0.5 1 1.5

Clo

sing

For

ce (k

ips)

Closing Displacement (in)

Fisher et al.FEM - FrictionFEM - Rough

66

0

-66-66

-44

-22

0

22

44

66

-8 -4 0 4 8

Dis

tanc

e fr

om M

id-D

epth

of G

irder

(in)

Change in Longitudinal Normal Stress (ksi)

Fisher et al.

FEM - Friction

FEM - Rough

Fisher at al. (Average)

FEM - Friction(Average)FEM - Rough(Average)


B-5





-66

-44

-22

0

22

44

66

-16 -8 0 8 16

Dis

tanc

e fr

om M

id-D

epth

of G

irder

(in)


Fisher et al.

FEM - Friction

FEM - Rough



-66

-44

-22

0

22

44

66

-16 -8 0 8 16

Dis

tanc

e fr

om M

id-D

epth

of G

irder

(in)


Fisher et al.

FEM - Friction

FEM - Rough




B-6

B.1.3 Calculation of Dynamic Amplification Factors 95

In order to characterize the inertial effects resulting from sudden failure of a primary tension component, 96 the ratio between the maximum stress (peak stress experienced during the dynamic event) and the final 97 stress (stress after inertial effects are dissipated) minus 1.0, was calculated at multiple locations so a critical 98 location was found; this being the reported maximum dynamic amplification factor. Two separate failure 99 scenarios were considered. First, sudden failure of girder G4 in the middle of the center span and second, 100 a sudden failure at the middle of the northernmost end span were modeled separately in two analyses. The 101 first scenario matched the failure that occurred in the field. 102

Sudden failure of girder G4 (fascia girder) in the middle of the center span resulted in a maximum 103 dynamic amplification factor of 0.39. Sudden failure of girder G4 in the middle of the northernmost end 104 span resulted in a maximum dynamic amplification factor of 0.26. Figure B-8 and Figure B-9 shows the 105 response of the undamaged girder (girder G3) after sudden failure of girder G4 at center span and end span, 106 respectively. 107

108

109 Figure B-8. Longitudinal normal stress at bottom flange of Girder G3 after sudden fracture of 110

Girder G4 at the middle of the center span. The results are calculated at the sections of Girders G3 111 closest to the fracture location. 112

10

15

20

25

30

0 2 4 6 8 10

Lom

gitu

dina

l Nor

mal

Stre

ss (k

si)

Time after Fracture (s)


B-7

113 Figure B-9. Longitudinal normal stress at bottom flange of Girder G3 after sudden fracture of 114 Girder G4 at the middle of the northern end span. The results are calculated at the sections of 115

Girders G3 closest to the fracture location. 116

B.1.4 Redundancy Evaluation 117

The capacity of the portion of the Neville Island Bridge under analysis was evaluated for the Redundancy 118 I and Redundancy II load combinations. In the analysis the failure of Girder G4 at the middle of the center 119 span and in the northernmost end span were considered separately. The results of the redundancy analysis 120 were evaluated according to the proposed failure criteria. Table B-1 and Table B-2 shows the most critical 121 results obtained from the redundancy analysis of the structure after failure at the center span and end span, 122 respectively. The structure showed adequate levels of redundancy after the fracture of Girder G4 at either 123 the center span or the end span by complying with the strength and displacement requirements in the 124 performance criteria. No plastic strain in excess over 0.01 were computed in any load case of the 125 Redundancy I and Redundancy II load combinations. Similarly, no concrete crushing was computed either. 126 The maximum vertical deflection for the failure of girder G4 in the center span was 21.5 inches, and 13.6 127 inches for the failure in the end span, both below the L/50 limit. These are summarized in Table B-3. 128

129 130

2

4

6

8

10

12

0 2 4 6 8 10

Lom

gitu

dina

l Nor

mal

Stre

ss (k

si)



B-8

Table B-1. Results obtained for redundancy evaluation of the Neville Island Bridge. Failure of 131 girder G4 in the center span. 132

Load Combination Redundancy I Redundancy II

Maximum Equivalent Plastic Strain in

Primary Members

Value 0.00299 0.00157 Location Top flange of girder G4 over Pier 9

Load Case 1 lane

Concrete Crushing Value

No concrete crushing in the slab Location Load Case

Maximum Vertical Reaction Force

Value 2569 kip 2135 kip Location Girder G4 over pier 10

Load Case 2 lanes 3 lanes

Maximum Horizontal Reaction Force


Load Case 1 lane

Maximum Horizontal Displacement at

Supports

Value 1.89 in Location Girder G4 over pier 10

Load Case 2 lanes 3 lanes Maximum Vertical

Deflection Value N. A. 21.5 in

133 134


B-9

Table B-2. Results obtained for redundancy evaluation of the Neville Island Bridge. Failure of 135 girder G4 in the end span. 136



Primary Members

Value 0.001439 0.000824 Location Top flange of girder G3 at failure section.



No concrete crushing in the slab Location Load Case



Load Case 2 lanes


Value 123 kip 53.1 kip Location Girder G3 over pier 10 Girder G3 over Pier 11

Load Case 1 lane


Supports

Value 0.923 in 0.634 in Location Girder G3 over pier 11



137

Table B-3. Redundancy evaluation of the Neville Island Bridge. 138

Performance Requirement

Most Critical Analysis Case Result Acceptable?

Strength Requirements

Steel Primary

Members

Failure at center span. Redundancy I. 1 lane loaded.

No component has strain larger than 5εy or 1%. Failure strain was not reached anywhere.

YES

Concrete Crushing - No concrete crushing in

the slab. YES

Serviceability Requirements

Vertical Deflection

Failure at center span. (Only Redundancy II

DL considered).

Maximum deflection is 21.5 in, which is lower

than L/50 (84 in) YES

Notes 1. The analysis showed that the structure was capable of resisting an additional 15% of the applied

factored live load. 2. In order to complete the evaluation, the displacements and reaction forces calculated at support

locations should be used as factored demands to check against the nominal capacity of the supports and substructure members.

139


B-10

B.1.5 Conclusions 140

A finite element model of the Neville Island Bridge was constructed and analyzed using the procedures 141 developed in this research. The model was successfully benchmarked against available filed observations 142 and data. This means that the finite element model captures the behavior of the portion of interest of the 143 Neville Island Bridge, including the alternative load-paths that develop after the failure of a tension 144 component. These alternative load-paths are provided by the interactions modeled, such as connections 145 among steel members, frictional contact between the slab and the steelwork and catenary action in the slab. 146

Dynamic analysis of the response of the structure after sudden failure of a single primary girder resulted 147 in maximum dynamic amplification of 0.39. Additionally, the proposed load combinations were applied 148 to evaluate the redundant capacity of the Neville Island Bridge after failure of a single girder. The results 149 were compared against the proposed performance criteria. The comparison revealed that the bridge meets 150 the strength and serviceability criteria. Therefore, the Neville Island Bridge would meet the proposed 151 performance requirements for system analysis. 152


B-11

B.2 Summary of Analysis Performed for the Hoan Bridge 153

The portion of the Hoan Bridge that has been analyzed is one of the northbound south approach structures 154 to the tied-arch span. This unit consists of three welded plate girders continuous over three spans, 217 feet 155 long each. In 2000, several cracks were detected in all three girders in the northernmost end span. The 156 cracks were initiated at details that were prone to develop constrained induced fracture (CIF). Two of the 157 cracks extended to full depth fractures in one of the exterior girders (Girder F) and the interior girder (Girder 158 E). Figure B-10 shows the locations were the cracks were detected; locations F28 and E28 had full depth 159 fractures. 160

161

162 Figure B-10. Location of cracks in the Hoan Bridge (from Connor et al. (2002) [2]). 163

Due to the large deflections resulting from the full depth fractures, the structure was closed and 164 demolished. During the failure investigation, J. W. Fisher et al. (2001) and R. J. Connor et al. (2002) 165 conducted testing to determine the cause of the failure and to design adequate repair and rehabilitation 166 procedures [2], [3]. Results from field tests in which instrumentation was installed and test trucks driven 167 across the mirrored spans of the bridge reported in R. J. Connor et al. (2002) were used to benchmark the 168 constructed finite element model. 169



• Three parallel plate girders modeled with shell elements. The girders were attached to connector 174 elements which simulated the effects of pier flexibility. 175


B-12

• A system of floor beams and lateral braces modeled with shell elements. The geometry of the 176 connections among floor beams, bracing and girder was explicitly model. 177

• Four stringers modeled with shell elements. The connection between the stringers and the floor 178 beams was modeled with a mesh tie constraint. 179

• A non-composite slab in which concrete was modeled with solid elements and rebar with embedded 180 truss element. Contact interaction that considers “hard” normal and frictional tangential behavior 181 was specified between the slab and the steelwork. 182

The bridge was analyzed using the procedures developed to compute dynamic amplification factors for 183 redundancy evaluation (DAR) and evaluate the structure for the Redundancy I and Redundancy II loading 184 combinations. Figure B-11 shows a detail of the geometry of the structure. 185

186

187 Figure B-11. Detail bottom view of the geometry of the Hoan Bridge finite element model: 188

concrete slab (grey), rebar (black), girders (blue), floor beams (red), stringers (magenta), lateral 189 bracing (green), connection details (orange). 190


Two analysis were carried out to determine whether the constructed finite element model captured the 192 behavior exhibited by the portion of interest of the Hoan Bridge. First, full depth fractures at Girder E and 193 Girder F were modeled while the structure was under dead load only in order to replicate the state of the 194 structure before its demolition. A deflection of 36 inches was calculated in the finite element analysis. 195 According to eyewitness reports, the deflection was estimated to be between 36 and 42 inches. (It is noted 196 that some reports indicate 48 inches.). Since the defections were not actually measured, the calculated 197 deflections under dead load are considered to be reasonable. The observed deflections may have been 198 larger than the ones computed in the finite element analysis because Girder D had large web cracks that 199 were not explicitly model in the analysis. 200

Secondly, strain gage measurements described in R. J. Connor et al. (2002) were used to benchmark the 201 constructed finite element model. The test was not conducted in the structure of interest but on a twin 202 structure located north of the tied-arch span of the Hoan Bridge [2]. The geometry of the twin structure is 203 almost mirrored, except that the spans measure 214 feet (instead of 217 feet). The loading and structural 204 conditions during the test were replicated in an analysis procedure applied to the constructed finite element 205 model. Table B-4 shows a comparison between the experimental values and the results of the finite element 206 analysis. The experimental test consisted of load tests in which a single three-axle truck was parked in the 207


B-13

striped lanes, one at a time. The location of the gages is shown in Figure B-12. The average error is 7.7% 208 approx. (maximum error is 15% approx.), which was considered to be satisfactory. 209

Considering both approaches to benchmarking the model yielded good correlation with observed 210 deflections and field measured strains, the approach for modeling the non-composite slab and the structural 211 steel is deemed reasonable. 212

Table B-4. Comparison between load test gage readings in Connor et al. (2002) [2] and results 213 from finite element analysis. All results are ksi. 214

Gage Member Connor et al. (2002) Finite Element Analysis

Lane 1 Loaded

Lane 2 Loaded

Lane 3 Loaded

Lane 1 Loaded

Lane 2 Loaded

Lane 3 Loaded

CH71 East Strut

0.26 0.35 0.43 0.28 0.36 0.48 CH72 -0.84 -0.73 0.38 -0.86 -0.76 0.40 CH73 0.19 0.26 0.36 0.20 0.30 0.39 CH74 SE

Diagonal

-0.17 0.05 0.49 -0.18 0.06 0.54 CH75 0.02 -0.05 -0.12 0.02 -0.06 -0.13 CH76 -0.11 0.08 0.44 -0.12 0.09 0.48 CH77

West Strut 0.27 0.41 0.33 0.30 0.43 0.37

CH78 0.21 0.29 0.24 0.22 0.31 0.24 CH79 0.60 -0.29 -0.85 0.69 -0.33 -0.97 CH80 SW

Diagonal

0.19 0.09 -0.04 0.19 0.10 -0.04 CH81 0.51 0.28 -0.15 0.57 0.29 -0.17 CH82 -0.16 -0.12 0.01 -0.17 -0.13 0.01 CH87 Web 0.55 0.69 0.59 0.58 0.75 0.65

CH88 Bot. Flange 0.84 1.11 0.99 0.91 1.16 1.00

215


B-14

216 Figure B-12. Location of strain gages in load test (from Connor at al. (2002) [2]). 217


B-15


In order to characterize the inertial effects resulting from sudden failure of a primary tension component, 219 the ratio between the maximum stress (peak stress experienced during the dynamic event) and the final 220 stress (stress after inertial effects are dissipated) minus 1.0, was calculated at multiple locations so a critical 221 location was found; this being the reported maximum dynamic amplification factor. For this simulation, 222 Girder E and Girder D were assumed to have failed separately. In other words, two analyses were 223 performed. The fractures were located at D28 for Girder D and E28 for Girder E as shown in Figure B-10. 224

Sudden failure of Girder D (exterior girder) resulted in a maximum dynamic amplification factor of 0.21 225 calculated at Girder E (interior girder). Sudden failure of Girder E resulted in a maximum dynamic 226 amplification factor of 0.19 calculated at Girder D. Figure B-13 and Figure B-14 show the response of the 227 intact girders after sudden failure of Girder D and Girder E, respectively. As expected, failure of Girder E, 228 the middle girder, results in identical amplification at the exterior girders. 229

230

231 Figure B-13. Longitudinal normal stress at bottom flange of Girder E and Girder F after sudden 232

fracture of Girder D. The results are calculated at the sections of Girders E and Girder F closest to 233 the fracture location. 234

0

5

10

15

20

25

30

-1 0 1 2 3 4 5

Long

. nor

m. s

tress

(ksi

)

Time after fracture (s)

Girder EGirder F


B-16

235 Figure B-14. Longitudinal normal stress at bottom flange of Girder D and Girder F after sudden 236

fracture of Girder E. The results are calculated at the sections of Girders D and Girder F closest to 237 the fracture location. 238


The capacity of the portion of the Hoan Bridge under analysis was evaluated for the Redundancy I and 240 Redundancy II load combinations. In the analysis only the failure of Girder D was considered as it was 241 deemed the most critical failure scenario. The results of the redundancy analysis were evaluated according 242 to the proposed failure criteria. Table B-5 shows the results obtained from the redundancy analysis of the 243 structure after failure of Girder D. The structure showed adequate levels of redundancy after the failure of 244 either Girder D by complying with the strength and displacement requirements in the performance criteria. 245 No plastic strain in excess over 0.01 were computed in any load case of the Redundancy I and Redundancy 246 II load combinations. Similarly, no concrete crushing was computed either. The maximum vertical 247 deflection for the failure of girder D was 10.3 inches, which is below the L/50 limit. These are summarized 248 in Table B-6. 249 250

0

5

10

15

20

25

30

-1 0 1 2 3 4 5

Long

. nor

m. s

tress

(ksi

)

Time after fracture (s)

Girder DGirder F


B-17

Table B-5. Results obtained for redundancy evaluation of the Hoan Bridge. 251



Primary Members

Value 0.0022 0.00077 Location Web of girder E at failure section.

Load Case 3 lanes


No concrete crushing in the slab. Location Load Case


Value 1941 kip 1511 kip Location Girder E over pier 3S

Load Case 3 lanes


Value 55.3 kip 58.7 kip Location Girder D over pier 2S.



Supports

Value 0.331 in 0.385 in Location Girder E over pier 2S.



252

Table B-6. Redundancy evaluation of the Hoan Bridge. 253




Steel Primary

Members

Redundancy I. 3 lanes loaded.


YES


the slab. YES


Vertical Deflection

(Only Redundancy II DL considered).






254


B-18


A finite element model of the Hoan Bridge was constructed and analyzed using the procedures developed 256 in this research. The model was successfully benchmarked against available filed observations and data. 257 This means that the finite element model captures the behavior of the portion of interest of the Hoan Bridge, 258 including the alternative load-paths that develop after the failure of a tension component. These alternative 259 load-paths are provided by the interactions modeled, such as connections among steel members, frictional 260 contact between the slab and the steelwork and catenary action in the slab. 261

Dynamic analysis of the response of the structure after sudden failure of a single primary girder resulted 262 in maximum dynamic amplification of 0.21. Additionally, the proposed load combinations were applied 263 to evaluate the redundant capacity of the Hoan Bridge after failure of a single girder. The results were 264 compared against the proposed performance criteria. The comparison revealed that the bridge meets the 265 strength and serviceability criteria. Therefore, the Hoan Bridge would meet the performance requirements 266 for system analysis. 267


B-19

B.3 Summary of Analysis on the UT Twin Tub Girder Bridge 268

The UT Tub Girder Bridge is a single span curved twin tub girder bridge. Figure B-15 shows the 269 overview of the bridge. The radius of curvature (at the bridge centerline) is 1,365.4 ft., the span (at the 270 bridge centerline) is 120 ft., and deck width is 23.3 ft. This bridge is consisted of five major components, 271 i.e., the concrete slab, concrete railings, twin tub girder system, shear studs that are used to develop the 272 composite actions between the tub girders and the concrete slab, and reinforcements for the concrete slab 273 and railings. The twin tub girder system is composed of two tub girders, web stiffeners, end diaphragms, 274 internal braces, constructional braces, and lateral braces. 275

276

277 Figure B-15. Geometry of the UT Tub Girder Bridge. 278



• Concrete deck and railings modeled with 3D solid elements. 283 • The webs and flanges of the steel tub girders, web stiffeners, and end diaphragms modeled using 284

4-node shell elements. 285 • Internal braces modeled using beam elements. 286 • Lateral braces modeled using two-node three-dimensional connector elements. 287 • Reinforcing steel modeled using 2-node linear truss elements. 288 • Embedded constraints to specify the interaction between the concrete slab and reinforcing bars. 289 • General contact to specify the interactions between: (1) the bottom side of the concrete slab and 290

the top flange of the tub girders, and (2) the railings (parapets) at the gaps (if the gaps are closed). 291 • Simplified beam-connector model to specify the axial and shear interaction between the shear studs 292

and concrete slab. 293


B-20

The bridge was analyzed using the procedures developed to compute dynamic amplification factors for 294 redundancy evaluation (DAR) and evaluate the structure for the Redundancy I and Redundancy II loading 295 combinations. Figure B-16 shows the finite element model of the bridge. 296

297

298 Figure B-16. Finite element model of the UT Tub Girder Bridge. 299


A three-step analysis was carried out to determine whether the developed finite element model captured 301 the behavior of the UT Tub Girder Bridge. In the first step, the webs and bottom flanges at the mid span 302 of the exterior girder fractured. In the second step, gravity loading was applied to the entire bridge. In the 303 third step, additional loading that simulated the loads in the test was applied. 304

Figure B-17 shows the comparisons of applied load-deflection curve of the exterior (fractured) girder 305 obtained from analysis and experimental test (conducted by the UT research team [4]). Figure B-18 also 306 compares the collapsed bridge observed from analysis and experimental test. As shown, the analysis can 307 predict the ultimate behavior of the bridge with the fracture. 308

Interior railing

Exterior railing

Concrete slab

Twin tub girder system


B-21

309 Figure B-17. Comparison of the load-deflection response of the exterior (fractured) girder 310

obtained from analysis and experimental test. 311

312 Figure B-18. Comparison of the collapsed bridge observed from analysis and experimental test. 313

The validity of the developed simplified beam-connector model for shear studs was also demonstrated 314 in the analysis. As shown in the analysis, with the load increased incrementally, stud pullout developed 315 along the exterior flange of the fractured girder, while the haunch separation developed along the interior 316 flange of the fractured girder, as shown in Figure B-19(a). This agrees with the observations made in the 317 experimental test, as shown in Figure B-19(b). Further detail regarding the research and benchmarking of 318 the shear stud tensile behavior can be found in Appendix A. 319

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

App

lied

forc

e, k

ips

Midspan deflection, in.

FEMEXP


B-22

320 Figure B-19. Haunch separation observed from analysis and experimental test. 321


In order to characterize the inertial effects resulting from sudden failure of a primary tension component, 323 the dynamic amplification factor (DAR) was calculated. The dynamic amplification factor was defined as 324 the ratio between the maximum stress (peak stress experienced during the dynamic event) and the final 325 stress (stress after inertial effects are dissipated) minus 1.0. Sudden failure of the exterior girder at the mid 326 span resulted in a maximum dynamic amplification factor of 0.30, which is coincident with the value of 327 0.30 reported by the UT Research Team [4]. Figure B-20 shows the response of the intact girder after 328 sudden failure. 329

330


B-23

331 Figure B-20. Longitudinal normal stress at bottom flange of the interior (intact) girder after 332

sudden fracture. 333


The capacity of the UT Twin Tub Girder Bridge was evaluated for the Redundancy I and Redundancy II 335 load combinations. The results of the redundancy analysis were evaluated according to the proposed failure 336 criteria. Table B-7 shows the results obtained from the redundancy analysis of the structure after failure at 337 the exterior girder. The structure did not satisfy the strength or performance criteria for the failure of the 338 exterior tub girder. In fact, the structure was not able to sustain the required factored live load as 339 summarized in ??? 340

Once failure if the exterior girder is introduced in the FEA, extended shear stud failure takes place along 341 the exterior girder causing it to drop and completely detach from the bottom of the slab. As the exterior 342 girder drops, it rotates leading to distortion of the end diaphragms, see Figure B-21. In the end, the bridge 343 becomes unstable and flips towards the exterior (radial outward direction), see Figure B-22. 344

0

10

20

30

40

50

0 1 2 3 4 5 6

Long

itudi

nal N

orm

al S

tress

(ksi

)



B-24

345 Figure B-21. Extensive shear stud failure and detachment of exterior girder from the slab. 346

347

348 Figure B-22. Excessive distortion of end diaphragms due to fall and rotation of exterior tub girder. 349

350


B-25

Table B-7. Results obtained for redundancy evaluation of the UT Tub Girder Bridge. 351



Primary Members

Value Rupture of end diaphragms takes place under factored

dead load only. Location Load Case


Extensive concrete crushing with development of hinging mechanism between the tub girders. Location

Load Case


Value Bridge becomes unstable and falls from supports. Location

Load Case



Load Case


Supports


Load Case Maximum Vertical

Deflection Value N. A. Unstable, non-computable.

352

Table B-8. Redundancy evaluation of the UT Tub Girder Bridge. 353




Steel Primary

Members

Redundancy I and Redundancy II.

No live load applied.

Excessive distortion of end diaphragms

resulting in rupture. NO

Concrete Crushing

Redundancy I and Redundancy II.

No live load applied.

Extensive crushing with hinging

mechanism in the slab. NO


Vertical Deflection

(Only Redundancy II DL considered). Structure is unstable. NO

Notes 1. The analysis was not completed as the structure was not able to reach static equilibrium after

the failure of the exterior tub girder under factored dead loads only. 2. Displacements and reaction forces could not be calculated at support locations as the bridge

flips and falls from it supports. 354


B-26


A finite element model of the UT Tub Girder Bridge was constructed and analyzed using the procedures 356 developed in this research. The model was successfully benchmarked against available filed observations 357 and data. This means that the finite element model captures the behavior of the portion of interest of the 358 UT Tub Girder Bridge, including the alternative load-paths that develop after the failure of a tension 359 component. These alternative load-paths are provided by the interactions modeled, such as connections 360 among steel members, frictional contact between the slab and the steelwork and catenary action in the slab. 361

Dynamic analysis of the response of the structure after sudden failure of a single primary girder resulted 362 in maximum dynamic amplification of 0.30, which replicates the value of 0.30 reported by the UT Research 363 Team [4]. Additionally, the proposed load combinations were applied to evaluate the redundant capacity 364 of the UT Tub Girder Bridge after failure of a single girder. The results were compared against the proposed 365 performance criteria. The comparison indicated that the bridge did not meet any criteria as it became 366 unstable after the failure of the exterior tub girder under factored dead loads only. Therefore, the UT Tub 367 Girder Bridge would not meet the proposed performance requirements for system analysis. 368


B-27

B.4 Summary of Analysis on the Milton Madison Bridge 369

The Milton Madison Bridge is a 19-span bridge comprised of various riveted truss configurations. It was 370 constructed over the Ohio River in 1921. The structure carries two lanes of traffic between Madison, 371 Indiana, and Milton, Kentucky. The portion of the bridge under study consists of a simple span symmetric 372 Pratt truss. Figure B-23 shows a photograph of the span under study. Each truss consisted of seven panels 373 that are 21 ft. in length; the total length of the truss from center to center of bearing is 147 ft. The 374 superstructure width is 24 ft., and the truss height is 22 ft. The deck system is located 4.75 ft. below the 375 top chord of the truss and consists of six lines of stringers spaced at 3.67 ft. on center. 376

Floor beams are attached below the upper truss joints and therefore are not coincident with the upper 377 truss joints. The original deck was removed from the bridge in 1996 and replaced with an exodermic deck 378 system consisting of an overlay that is composite with the stringers and floor beams. This was a precast, 379 partially filled grid deck system. Once the precast segments were installed, an overlay and cast-in-place 380 curb were placed to finish assembly of the new deck. Details pertaining to the deck and structural 381 configuration are provided in Diggelmann et al. [5]. The bottom chord of Span L3-L4 at the upper stream 382 was fractured to evaluate the redundancy of this bridge (see Figure B-23). 383

384

385 Figure B-23. Geometry of the Milton Madison Bridge and fracture location. 386


Detailed 3D finite element model was developed in accordance with the proposed FEA methodology for 388 system analysis. The geometry and nominal material properties input in the analysis were as described in 389 the design plans. The model was composed of: 390

• Concrete deck modeled with 3D solid elements. 391


B-28

• Main truss members (i.e., top chord, bottom chords, and diagonal members), floor beams, stringers, 392 lateral bracing, and steel beams in the exodermic concrete slab modeled using 4-node shell 393 elements. 394

• Embedded constraints to specify the interaction between the concrete slab and steel beams. 395 The bridge was analyzed using the procedures described to compute dynamic amplification factors 396

(DAR) for redundancy evaluation and evaluate the structure for the Redundancy I and Redundancy II 397 loading combinations. Figure B-24 shows the finite element model of the bridge. 398

399

400 Figure B-24. Finite element model of the Milton Madison Bridge. 401


An analysis was carried out to determine whether the developed finite element model captured the 403 behavior of the Milton Madison Bridge. Results from the analysis were compared to the experimental tests 404 results obtained by Diggelmann et al. [5], including the stresses (in the main truss members, stringers, floor 405 beams, and lateral bracings) before and after fracture, dynamic amplification factors, and vertical 406 deflections. Details of the benchmarking have been presented by Cha et al. [6]. 407


In order to characterize the inertial effects resulting from sudden failure of a primary tension component, 409 the dynamic amplification factor (DAR) was calculated based on the results reported by Cha et al. [2]. The 410 dynamic amplification factor was defined as the ratio between the maximum stress (peak stress experienced 411 during the dynamic event) and the final stress (stress after inertial effects are dissipated) minus 1.0. Sudden 412

L0

L1

L2

L3

L4

L5

L6

L7

U0U1

U2

U3

U4

U5

U6

U7

Upstream (US)

Downstream (DS)

Fracture


B-29

failure of the lower chord at the mid span resulted in a maximum dynamic amplification factor of 0.36. 413 This was observed in the diagonal U4US-L3US. 414


The portion of the Milton Madison Bridge under analysis was evaluated for the Redundancy I and 416 Redundancy II load combinations. Results of the redundancy analysis were evaluated according to the 417 proposed performance criteria. Table B-9 shows the results obtained from the redundancy analysis of the 418 structure after the sudden fracture. The structure showed adequate levels of redundancy after the fracture 419 of the exterior girder from the comparisons with the strength and displacement requirements in the 420 performance criteria. 421

The largest equivalent plastic strain computed was 0.0029 at the connection between bottom chord and 422 Stringer L3US-L3DS on the downstream when the bridge was subjected to Redundancy I load combination 423 (one lane). No concrete crushing was observed in the model after the fracture of in both load combinations. 424 The maximum vertical deflection (0.82 in.) is below L/50 (35 in.) and the maximum change in cross-slope 425 (0.28%) is below 5%. A summary of the redundancy evaluation is shown in Table B-10. 426

Table B-9. Results obtained for redundancy evaluation of the Milton Madison Bridge. 427



Primary Members

Value 0.0029 0.00023

Location Downstream: connection between bottom chord and Stringer L3US-L3DS

Load Case 1 lane 2 lanes


No concrete crushing in the slab. Location Load Case


Value 566 kip 497 kip Location Both end supports

Load Case 2 lanes


Value Structure is roller supported. Location

Load Case


Supports

Value 0.62 in 0.69 in Location L7US

Load Case 1 lane Maximum Vertical


428

429


B-30

Table B-10. Redundancy evaluation of the Milton Madison Bridge. 430




Steel Primary

Members

Redundancy I. 1 lane loaded.


YES


the slab. YES


Vertical Deflection

(Only Redundancy II DL considered).






431


A finite element model of the Milton Madison Bridge was constructed and analyzed using the procedures 433 developed in this research. The model was successfully benchmarked against experimental data. This 434 means that the finite element model captures the behavior of the portion of interest of the Milton Madison 435 Bridge, including the alternative load-paths that develop after the failure of a tension component. 436

Cha et al. (2014) [6] reported that the response of the structure after sudden failure of the lower chord 437 resulted in maximum dynamic amplification of 0.36. Additionally, the proposed load combinations were 438 applied to evaluate the redundant capacity of the Milton Madison Bridge after failure of the lower chord. 439 The results were compared against the proposed performance criteria. The comparison revealed that the 440 bridge meets the strength and most of the serviceability criteria. Therefore, the Milton Madison Bridge 441 would meet the proposed performance requirements for system analysis. 442


B-31

B.5 Summary of Analysis on the White River Bridge 443

Built in 1958, the White River Bridge (NBI#14560) is comprised of two, sixteen span, two-girder riveted 444 superstructures sharing a single substructure. Each superstructure carries two lanes of either northbound or 445 southbound US-41 traffic over the White River and adjacent north and south floodplains. The bridge is 446 located near Hazleton, IN. Figure B-25 shows a partial elevation of the northbound bridge. The US-41 447 White River Bridge is symmetric about its midpoint and has a total length of 2403 ft. The 16 spans of each 448 superstructure consist of equal end spans of 111.25 ft. and 14 interior spans of 155.75 ft. Both 449 superstructures have a width of 32.5 ft. The bridge also has four pin and hanger expansion joints spread 450 throughout the length. 451

452

453 Figure B-25. Geometry of the White River Bridge and fracture location. 454



• Concrete deck modeled with 3D solid element and embedded truss element modeling steel 459 reinforcement. 460

• Main girders and floor beams modeled using 4-node shell elements. 461 • Reinforcing steel modeled using 2-node linear truss elements. 462 • Embedded constraints to specify the interaction between the concrete slab and steel reinforcement. 463 • General contact to specify the interactions between the bottom side of the concrete slab and the top 464

flange of the main girders and floor beams. 465 The bridge was analyzed using the procedures developed to compute dynamic amplification factors for 466

redundancy evaluation (DAR) and evaluate the structure for the Redundancy I and Redundancy II loading 467 combinations. Figure B-26 shows the finite element model of the bridge. 468


B-32

469 Figure B-26. Finite element model of the White River Bridge. 470


Finite element analysis was carried out to determine whether the developed finite element model captured 472 the behavior of the White River Bridge. Results from the analysis were compared to the results from the 473 static load tests and crawl tests conducted by obtained by Sherman et al. [7]. Details of the benchmarking 474 were presented by the RT in Cha [8]. 475


In order to characterize the inertial effects resulting from sudden failure of a primary tension component, 477 the dynamic amplification factor (DAR) was calculated. The dynamic amplification factor was defined as 478 the ratio between the maximum stress (peak stress experienced during the dynamic event) and the final 479 stress (stress after inertial effects are dissipated) minus 1.0. Sudden failure of the exterior girder at the mid 480 span resulted in a maximum dynamic amplification factor of 0.32 at bottom flange of Span N (Girder 1) at 481 the mid span. 482


A finite element model of the White River Bridge was constructed and analyzed using the procedures 484 developed in this research. The model was successfully benchmarked against experimental data. This 485 means that the finite element model captures the behavior of the portion of interest of the White River 486 Bridge, including the alternative load-paths that develop after the failure of a tension component. Dynamic 487 analysis of the response of the structure after sudden failure of a single primary girder resulted in maximum 488 dynamic amplification of 0.32. 489

Span M

Span N

Span P

Span Q

Girder 2

Girder 1 Fracture


B-33

B.6 Summary of Analysis on the Dan Ryan Bridge 490

The Dan Ryan Expressway provides direct railway transit between the 95th street terminal to the loop in 491 Chicago. Cracks were observed at Bents No. 24-26 in January 1978. The portion of the bridge being 492 evaluated in this report is the section between Bent No. 24 and No. 25, and is referred to as the “Dan Ryan 493 Bridge” hereafter. Figure B-27 shows the overview of the bridge. The radius of curvature (at the bridge 494 centerline) is 400 ft., the span (at the bridge centerline) is 118.5 ft. This bridge is consisted of six major 495 components, i.e., the concrete slab, railings, plate girder system, cross girders, shear studs that are used to 496 develop the composite actions between the tub girders and the concrete slab, and reinforcements for the 497 concrete slab and railings. The Dan Ryan system is composed of four plate girders and lateral braces. 498

499

500 Figure B-27. Geometry of the Dan Ryan Bridge and fracture location. 501

The finite element model of the Dan Ryan Bridge was only develop to calculate dynamic amplification 502 factor after the failure of a cross girder. Unfortunately, there were no field test which data could have been 503 employed for benchmarking. Additionally, since it is a structure designed to carry light commuter trains, 504 the proposed load models, load combinations and performance criteria are not applicable for the evaluation 505 of system-level redundancy. 506


Detailed 3D finite element model was developed in accordance with the proposed FEA methodology for 508 system analysis. The geometry and nominal material properties input in the analysis were as described in 509 the design plans. The model was composed of: 510

• Concrete deck modeled with 3D solid elements. 511

Crack


B-34

• The webs and flanges of the plate girders and cross girders, and the stiffeners modeled using 4-512 node shell elements. 513

• Lateral braces modeled using two-node three-dimensional connector elements. 514 • Reinforcing steel modeled using 2-node linear truss elements. 515 • Embedded constraints to specify the interaction between the concrete slab and reinforcing bars. 516 • General contact to specify the interactions between: (1) the bottom side of the concrete slab and the 517

top flange of the plate girders, and (2) the railings (parapets) at the gaps (if the gaps are closed). 518 • Simplified beam-connector model to specify the axial and shear interaction between the shear studs 519

and concrete slab. 520 The bridge was analyzed using the procedures described to compute dynamic amplification factors 521

(DAR). The Redundancy I and Redundancy II loading combinations were not evaluated because they are 522 not applicable to railway bridges. Figure B-2 shows the finite element model of the bridge. 523

524

525 Figure B-28. Portion of the finite element model of the Dan Ryan Bridge. 526


In order to characterize the inertial effects resulting from sudden failure of a primary tension component, 528 the dynamic amplification factor (DAR) was calculated. The dynamic amplification factor was defined as 529 the ratio between the maximum stress (peak stress experienced during the dynamic event) and the final 530 stress (stress after inertial effects are dissipated) minus 1.0. Sudden failure of the two cross girders (Bent 531 No.24 and No. 25) resulted in a maximum dynamic amplification factor of 0.19. The response of the most 532 critical component in the structure after brittle failure of the cross girder is shown in Figure B-29. 533

Plate Girder: G127G128

G129G130

Cross Girder: Bent 25

Cross Girder: Bent 24


B-35

534 Figure B-29. Longitudinal normal stress at bottom flange of most critical component for the Dan 535

Ryan Bridge. 536


A finite element model of the Dan Ryan Bridge was constructed and analyzed using the procedures 538 developed in this research. Dynamic analysis of the response of the structure after sudden failure of a single 539 primary girder resulted in maximum dynamic amplification of 0.19. 540

Since the Dan Ryan Bridge carries commuter rail traffic, the condition of the bridge in the faulted state 541 was not compared to performance criteria developed herein. Rather, the analysis was used to gain further 542 insight into benchmarking and modeling techniques. Since the response was accurately predicted by the 543 model, further confidence is gained in the approaches developed and subsequently recommended for system 544 analysis. 545


B-36

B.7 List of References 546

[1] J. W. Fisher, A. W. Pense, J. D. Wood, J. H. Daniels, B. T. Yen, D. A. Thomas, H. Hausammann, 547 W. Herbein, B. R. Somers, and H. T. Sutherland, “Evaluation of the Fracture of the I79 Back 548 Channel Girder and the Electroslag Welds in the I79 Complex,” Bethlehem, PA, 1980. 549

[2] R. J. Connor and J. W. Fisher, “Report of Field Measurements and Controlled Load Testing of the 550 Hoan Bridge (I-794). ATLSS Report No. 02-01,” Bethlehem, PA, 2002. 551

[3] J. W. Fisher, E. J. Kaufmann, W. Wright, Z. Xi, H. Tjiang, B. Sivakumar, and W. Edberg, “Hoan 552 Bridge Forensic Investigation Failure Analysis Final Report,” Bethlehem, PA, 2001. 553

[4] B. J. Neuman, “Evaluating the Redundancy of Steel Bridges: Full Scale Destructive Testing of a 554 Fracture Critical Twin Box-Girder Steel Bridge,” Austin, TX, 2009. 555

[5] L. . Diggelmann, R. J. Connor, and R. J. Sherman, “Evaluation of member and load-path redundancy 556 on the US-421 Bridge over the Ohio River, Federal Highway Administration (FHWA) Publication 557 No. FHWA-HRT-13-105,” Turner-Fairbank Highway Research Center, McLean, VA., 2012. 558

[6] H. Cha, L. Lyrenmann, R. J. Connor, and A. H. Varma, “Experimental and Numerical Evaluation 559 of the Postfracture Redundancy of a Simple Span Truss Bridge,” J. Bridg. Eng., vol. 19, no. 11, 560 2014. 561

[7] R. Sherman, J. Mueller, R. Connor, and M. Bowman, Evaluation of effects of super-heavy loading 562 on the US 41 Bridge over the white river, JTRP Report C-36-56RRRR. 2012. 563

[8] H. Cha, “Life-Cycle of Steel Bridges: Effects of Local Damage due to Overweight Truck Traffic,” 564 Purdue University, 2014. 565

566

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