Inspection and Management of Bridges with Fracture-Critical Details (2005)

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68 1. Idriss, R.L., K.R. White, and D.V. Jauregui, “After-Fracture Response of a Two-Girder Steel Bridge,” Natural Hazards Mitigation, Presented at the Structures Congress ‘93, Irvine, Calif., Apr. 19–21, 1993. Idriss et al. (1) developed a computer model to study the after-fracture response of I-40 two-girder bridges. Field test data (2) were used to validate or modify the analytical model. The main focus of the analysis was to investigate the way in which the load distributes, the maximum load the bridge could withstand, and the potential for the bridge to collapse after a full-depth crack was introduced in one of the bridge girders. The analysis showed that the structure remained stable after the crack was introduced. The stability of the structure was attributed to a large surge in the tension force of the lateral bracing, which helped in stiffening and stabilizing the structure. 2. Idriss, R.L., K.R. White, C.B. Woodward, and D.V. Jauregui, “After-Fracture Redundancy of Two-Girder Bridge: Test- ing I-40 Bridges Over Rio Grande,” Conference Proceedings 7, Fourth International Bridge Engineering Conference, San Francisco, Calif., Aug. 28–30, 1995, pp. 316–326. Idriss et al. (2) conducted field testing on I-40 bridges over the Rio Grande in Albuquerque, New Mexico. The bridges were built in 1963 and were classified by AASHTO as nonredundant fracture critical. Similar to the intention of the analytical model (1), the main focus of the authors was to study the redistribution of loads, the load capacity the bridge can withstand, and the potential for collapse. The bridges were loaded in the positive moment region with a truck that was 95% of New Mexico legal load, and roughly equivalent to HS-18.35. The truck load was placed on the bridge four different times as four different levels of damage were introduced in one of the girders in the bridge. The fourth level of damage was such that a 6-ft crack was introduced in one of the 10-ft girders. The crack stretched to include the bottom flange, which was totally severed (only 4 ft of the web and the top flange were left to carry the bridge). Idriss et al. reported that under dead and live loads, and when the truck was located above the crack, the flange deflected 13/16 in. There was no sign of yielding, with no significant change in strains experienced by the gauged members until the bottom flange was completely severed. In other words, load redistribution did not occur until the bottom flange was completely severed. Another important finding was that most of the load was redistributed through the damaged girder and stringer deck system to the interior supports. In general, the load was redistributed through the damaged girder, the diagonals, the stringers, the deck, and the floorbeams. 3. Idriss, R.L. and K.R. White, “Secondary Load Paths in Bridge Systems,” Transportation Research Record 1290, Trans- portation Research Board, National Research Council, Washington, D.C., 1991, pp. 194–201. Idriss and White (3) studied the secondary load path in a four-girder bridge using finite-element analysis. The focus of the study was to investigate the distribution of the loads and the secondary load paths along which a load is transmitted when dam- age occurs in the given set of proportionate structures. Three finite-element analyses were conducted and the results were com- pared with experimental results from an AASHTO road test conducted in the early 1960s on four bridges. The load-deflection response showed good agreement between the finite-element model and the experimental results up to the load causing the first plastic hinge. Beyond that point, the actual structure showed much greater deflection than the model. The analysis was also conducted with three types of defects modeled at midspan in one of the two exterior girders. The first defect was a 50% loss in the flange section for a distance of 5 ft 6 in. at about the centerline of the girder, whereas the second defect was a 100% loss. The third defect included a crack at midspan in the bottom flange extending upward through the full depth of the web plate. The first sign of an excessive yielding with a plastic hinge was observed in the defec- tive girder. The more extensive the damage in the girder, the more widespread and extensive the yielding in the slab and diaphragms. When a near-full-depth crack was modeled at midspan, the maximum capacity of the bridge was 1.5 to 3 times an HS-20 truck loading. APPENDIX D Annotated Bibliography

69 4. Sweeney, R.A.P., “Importance of Redundancy in Bridge-Fracture Control,” Transportation Research Record 711, Trans- portation Research Board, National Research Council, Washington, D.C., 1979, pp. 23–30. Sweeney (4) discussed the importance of redundancy in controlling the fracture of bridges. He characterized welded structures to be generally not “fail-safe” in which, if cracks starts to run in a weld, it will not stop unless it runs out of mate- rial, weld, or driving force. Riveted structures however are internally member redundant because most members are built up of several components. Also, the holes provided in a riveted structure serve as crack stoppers at the interface between components. Using examples of bridges that had failed, Sweeney emphasized that designers of welded nonredundant struc- tures must ensure that no brittle fracture will occur during the life of a bridge. Sweeney also mentioned that fires have shown that trusses have considerable redundancy or an alternate load path that will prevent collapse by brittle fracture. 5. Lai, L.L.-Y., “Impulse Effect on Redundancy of a Tied-Arch Bridge,” Computing in Civil Engineering, Proceedings of the First Congress held in conjunction with A/E/C Systems ‘94, Washington, D.C., June 20–22, 1994. Lai (5) studied the redundancy of a tied arch bridge using a three-dimensional finite-element model. In a tied arch bridge the tie is always in tension and is classified as a fracture-critical member. In other words, if one of the ties fractures, the bridge will not be able to carry the load and will eventually collapse. Lai used a static incremental study to determine the degree of redundancy of the structure and found that after the fracture of the one of the ties, the structure can carry its own weight plus 1.3 times HS-20 truck loading without catastrophic collapse. Lai also considered the dynamic and impulse effect on the behav- ior of the bridge after the fracture of one of the ties. The dynamic analysis of the structure with unfractured ties showed that the first four modes of vibrations are 1.57, 1.82, 3.2, and 3.31 Hz, respectively. With one of the ties fractured, the natural fre- quencies changed to 1.29, 1.69, 2.73, and 2.89 Hz, respectively. Clearly, the reduction in the structural stiffness resulted in a reduction in the natural frequencies. When considering the impulse loading, the maximum deflection of the fractured struc- ture was calculated to be twice as much as that when using static incremental analysis. 6. Pandey, P.C. and S.V. Barai, “Structural Sensitivity as a Measure of Redundancy,” Journal of Structural Engineering, Vol. 123, No. 3, 1997, pp. 360–364. Pandey and Barai (6) presented a definition of redundancy based on response sensitivities where the generalized redundancy is inversely proportional to the elements’ response sensitivity In their def- inition the redundancy of the structure is no longer a fixed quantity, but rather a function of the strength and the response of the structure at a given stage. 7. Hartley, D. and S. Ressler, “After-Fracture Redundancy of Steel Bridges: A Review of Published Research,” ATLSS Report No. 89-13, Lehigh University, Bethlehem, Pa., 1989. Hartley and Ressler (7) conducted a review of 16 articles and technical reports on the after-fracture redundancy of steel bridges. They concluded that no actual consistent definition of the word redundancy had been determined. As they mentioned, this could be because redundancy is characterized by a certain degree of inherent variability, which is very hard to quantify. 8. Csagoly, P.F. and L.G. Jaeger, “Multi-Load Path Structures for Highway Bridges,” Transportation Research Record 711, Transportation Research Board, National Research Council, Washington, D.C., 1979, pp. 34–39. Csagoly and Jaeger (8) provided a framework of reference for discussion of multiload path structures with the intention that such discussion will result in the elimination in future design of single-load path structures. Csagoly and Jaeger pro- vided various examples of bridges that behaved “unintentionally” as multiload path structures as a result of having backup systems that prevented collapse when critical components of the structures failed. It is worth mentioning that the authors characterized single-cell steel box girders as single-load path structures, suggesting that their future design should be eliminated. 9. Frangopol, D.M. and J.P. Curley, “Effects of Damage and Redundancy on Structure Reliability,” Journal of Structural Engineering, Vol. 113, No. 7, 1987, pp. 1533–1549. Frangopol and Curley (9) used an example of redundant and nonredundant trusses to illustrate that the degree of redundancy is not an adequate measure of the system’s overall strength. Rather, the strength measure is constituted by the behavior of the members (i.e., ductile versus brittle). Generalized redundancy Response sensitivi α 1 ty ⎛ ⎝⎜ ⎞ ⎠⎟ .

Frangopol and Curley recognized the need for the development of a better understanding and definition of redundancy in various types of bridges and used illustrative examples to define new ideas regarding redundancy in bridges. They defined the term R (the redundant factor for a bridge) as where Lintact defines the overall collapse load of the bridge without damage, whereas Ldamaged defines the overall collapse load of the damaged bridge. Therefore, R is the reserve strength between the component(s) damage and system collapse. They also stated that “important members could be identified in which their failure or severe damage would have a greater influence on the effec- tiveness of the redundancy of the bridge, and that more inspection and quality assurance should be given to such members.” 10. The Task Committee on Redundancy of Flexural Systems of the ASCE–AASHTO Committee on Flexural Members of the Committee on Metals of the Structural Division, “State-of-the Art Report on Redundant Bridge Systems,” Journal of Structural Engineering, Vol. 111, No. 12, Dec. 1985. The Task Committee on Redundancy of Flexural Systems (10) recognized that “loads are carried by the system along a vari- ety of simultaneous paths” and that “redundant load paths exist in most structures.” That being said, they examined methods to determine the redundant path in flexural systems and presented the experiences of approximately 100 bridges. The follow- ing highlights what they discussed. • Various analytical techniques could be used to investigate the linear elastic response of damaged flexural systems to loads that include reverse design using AASHTO; more sophisticated methods than AASHTO; and finite-difference, finite-strip, or finite-element methods. Nonlinear analysis for all critical stresses and deformations must be accurately determined. • Welded members can suffer a failure as a result of excess stress that is the result of an imperfection in the weld. • If several load paths are available in a structure, then weakening in the most critical location would be followed by a redistribution of the load in which the redistribution is a function of the changing stiffness of the structure. • Steel stringer bridges are highly redundant for the load for which they were designed. • Failure of one girder in a two-girder system may lead to collapse. However, large deflections could be the result of the redistribution of loads. • Secondary members are often not included in the analysis for the transverse behavior. They are also not considered in the analysis for live load. However, these members could participate in the load redistribution resulting in reduction of the stresses in the main members. • Fatigue cracks do not cause a change in the stiffness of the structure. However, if the crack length becomes critical, a sudden failure of the girder could take place. If the girder fails, then a drastic redistribution of the load to the adjacent girder would occur through the slab and the bracing systems. • Fatigue is the most common cause of reported damage in bridges. • Failure in bolted structures is unlikely to occur because if a crack originates it cannot propagate past the holes used for bolting. • Behavior of the bridge superstructure is not greatly affected if the skew angle is more than 60 degrees. • For loads up to the elastic limit, a fully composite interaction between the deck and the main girder could be assumed if the AASHTO code is used for the design even if the bridge is noncomposite. • Based on previous studies, in composite bridges the reinforced concrete deck is likely to be the first component to exhibit nonlinearity. • Bottom lateral wind bracing does not contribute greatly to live-load redistribution in straight bridges. The contribution of the bracing system to the load redistribution is high for curved girders. • Data on steel bridges that suffered damage indicate that if redundancy is present then few steel bridges would collapse. Furthermore, those bridges that collapsed were mostly nonredundant truss bridges. 11. Frangopol, D.M. and J.P. Curley, “Effects of Redundancy Deterioration on the Reliability of Truss Systems and Bridges,” Conference Proceeding, In Effects of Deterioration on Safety and Reliability of Structures, S. Marshall Ma, Ed., 1986. The definition of structural redundancy including system reliability and damage assessment concept was utilized to analyt- ically investigate the effect of redundancy deterioration on the reliability of truss systems and bridges. Using Figure D1, Frangopol and Curley (11) illustrated that the degree of redundancy of a system is not an adequate measure of system strength. The example showed that the redundant truss has an increase in ultimate load capacity compared with the nonredundant truss of 78%, 100%, and 131% for brittle, ductile and hardening behavior of members, respectively. R L L L = − intact intact damaged 70

71 Because the degree of redundancy of a system is not an adequate measure of system strength, Frangopol and Curley (11) introduced the redundancy factor R for bridges, which is the reserve strength between component(s) damage and system col- lapse. The redundancy factor R is equal to 1 when the damaged bridge has no reserve strength where R = Lintact/(Lintact − Ldamage) = λ/(λ − λ*), Lintact = the overall collapse load of the bridge without damage = λL, Ldamage = the overall collapse load of the damaged bridge = λ*L, and L = applied load on the bridge. Using this equation with various damage factors, which represent the percent reduction in the load carrying capacity of a given member, the redundant factor R could then be calculated. The results are helpful in that it makes it possible to identify which member or group of members are critical in the structure. 12. Frangopol, D.M. and R. Nakib, “Redundancy Evaluation of Steel Girder Bridges,” 5th International Conference on Struc- tural Safety and Reliability, San Francisco, Calif., Aug. 7–11, 1989. Considering corrosion damage scenarios, Frangopol and Nakib (12) reviewed several definitions of redundancy factors of existing steel girder bridges. Furthermore, an analytical model was developed to study the degree of redundancy of E-15-AF Colorado State Bridge in the presence of corrosion damage using the definition of the redundancy factor R provided in (11). 13. Frangopol, D.M. and K. Yoshida, “Loading and Material Behavior Effects on Redundancy,” Proceedings of Structures Congress, Chicago, Ill., Apr. 15–18, 1996. Frangopol and Yoshida (13) used a numerical example of a three-bar system to show that system redundancy could be greatly affected by variation in the applied load and/or material behavior. The angle in which the load was applied varied between 0° and 360°, whereas the material behavior was altered by choosing four different values, 0.25, 0.50, 0.75, and 1.00, to represent the yield stress ratio “a,” where “a” is defined as the tension yield stress to the compression yield stress . Failure loci were then generated with respect to first yielding and collapsing the system. Collapse and first yield loads (PC and PY) were represented by the distance between the origin and the collapse loci and the origin and the first yield loci, respectively. The redundancy factor R1 is then defined as: 14. Kudsi, T.N. and C.C. Fu, “Redundancy Analysis of Existing Truss Bridges: A System Reliability Approach,” First Inter- national Conference on Bridge Management, Barcelona, Spain, July 14–17, 2002. Kudsi and Fu (14) developed a new approach to the redundancy of structural systems in general bridges and truss bridges in particular. The approach consists of building a block diagram, which accounts for the degree of redundancy of the system and R P P PC Y C1 = −( ) σ σy C y T( ) Indeterminate Determinate (b) All Bars A = 72 in2 E = 29000 ksi FY = 36 ksi PY = 72 kips 4 5 31 2 1 4 5 6 2 (a) 96 in . 3 72 in. 72 in. FIGURE D1 Two elementary trusses (ref. 11 in Appendix D).

the possible amount of redundant members’ combinations (in parallel configuration) to be laid in series with the nonredun- dant members in the system. Multiple failure modes are then defined and equations are implemented to obtain the system’s pre- and post-failure reliability index and probability of failure, where the post-failure phase is defined as the phase when a member fails without causing collapse. The system is then defined as redundant or nonredundant by comparing the reliability index of the system after the failure of a particular member with the target reliability index. 15. Kritzler, R.W. and J. Mohammadi, “Probabilistic Evaluation of Redundancy of Bridge Structures,” Proceedings of the Sixth Specialty Conference, sponsored by the Engineering Mechanics, Structural, and Geotechnical Divisions of the American Society of Civil Engineers, Denver, Colo., July 8–10, 1992. Knowing that redundancy of structures could result from the reserve capacity of its members when stressed beyond their yield or buckling strength, Kritzler and Mohammadi (15) defined redundancy as “the degree of reverse strength available for pre- venting failure of an entire structural system.” They evaluated the degree of redundancy of bridges based on the difference between the safety index of the redundant structure, considering all of its failure paths and the safety index of the exact same structure with no alternative load path where redundancy measure is computed by subtracting the damage safety index (βs) from the controlling component safety index (βf) (the controlling component safety index is calculated based on the probabil- ity of failure of one component of the system.) 16. Heins, C. and C.K. Hou, “Bridge Redundancy: Effect of Bracing,” Journal of the Structural Division, Vol. 106, No. 6, June 1980, pp. 1364–1367. Like many others, Heins and Hou (16) realized the need for examining the effect of bracing members in bridge structures on the load distribution of two-girder and multigirder systems after the development of a crack in one of the girders. This was done using an analytical space frame model in which the flanges are supported by vertical and diagonal web plates. The girders were stiffened by transverse diaphragms and lateral wind bracing. The cracks were introduced in the flanges of the girders by assign- ing a negligible stiffness to small beam element. A two-system girder and a three-girder system with different spans were used in the study. The systems were examined by first assuming a cracked bottom flange, and then cracked bottom and top flanges. The results revealed that when one crack develops and no bracing is used, the deformation increases by 40% for the two-girder system and 10% for the three-girder system. However, if bracings are considered, the deformation increases by 10% for the two- girder system, although almost no increase in the deformation is noticed in the three-girder system. 17. Heins, C.P. and H. Kato, “Load Redistribution of Cracked Girders,” Journal of the Structural Division, Vol. 108, No. 8, Aug. 1982, pp. 1909–1915. An analytical model was employed by Heins and Kato (17) to study the effect of bracing on load distribution in a two-girder bridge system when one of the girders is damaged. The two-girder system consisted of two longitudinal girders with cross floor beams and longitudinal stringers. The flanges, the webs, and the deck slab were idealized as a series of intersecting beam elements. A crack was introduced near the center span of the girder with the assumption that the web elements along the crack had zero stiffness. Such an assumption is conservative, resulting in deformations and stresses higher than those that would develop in an actual damaged bridge. The result of the analysis showed that for a 120-ft girder the deformation of the cracked girder was reduced by 39% when bottom bracings were incorporated in the analysis, whereas the uncracked girder had a 19% increase in its deformation when the bottom bracings were used. For a 180-ft girder, the deformation of the cracked girder was reduced by 54% when bottom bracings were incorporated in the analysis, whereas the uncracked girder had a 20% increase in its deformation when the bottom bracings were used. 18. Tang, J.P. and J.T.P. Yao, “Evaluation of Structural Damage and Redundancy,” Conference Proceedings, In Effects of Damage and Redundancy on Structural Performance, D.M. Frangopol, Ed., American Society of Civil Engineers, New York, N.Y., 1987. Realizing that the material properties and the damage state of a structure is random in nature, Tang and Yao (18) interrelated the system strength, redundancy, structural damage, and member damage such that the random nature of strength and damage could be considered. 19. Furuta, H., M. Shinozuka, and J.T.P. Yao, “Probabilistic and Fuzzy Representation of Redundancy in Structural Systems,” Presented at the First International Fuzzy Systems Associated Congress, Palma de Mallorca, Spain, July 1985. As stated by Furuta et al. (19), the ultimate strength of a damaged structure is better measured by the residual resistance factor (RIF) and the redundant factor (RF) 72

73 where Xi = member properties of the ith member, Yj = reduction in geometry properties of the jth member (zero for undamaged structure), and Ak = constant representing original geometrical properties of the kth member. These equations assume that material properties, original geometry properties, and the damage level of a member are known. However, because such information is difficult to obtain, Tang and Yao (18) considered a probabilistic approach and treat some of the variables as random variables and define RIF and RF in the average sense where where E [.] denotes expected value. 20. Moses, F., “Evaluation of Bridge Safety and Remaining Life,” Conference Proceeding, In Structural Design, Analysis, and Testing, Alfred H.S. Ang, Ed., American Society of Civil Engineers, New York, N.Y., 1989, pp. 717–726. Based on reliability principles and available data, Moses (20) considered the overstress limit state and the fatigue limit state for the evaluation of bridges. The overstress limit state refers to the extreme event in which the maximum load effect exceeds the bridge strength capacity. The fatigue limit state is determined by repetitive loading and is more sensitive in steel bridges. Provided that the bridge is redundant in which a multiload path exists in the bridge, a target reliability index of 2.3 was chosen by the author. The reliability index b was calculated using the formula β = g_/σg, where g_ = mean safety margin, and σg = standard deviation of g. The value of g is calculated based on the safety index model: where R = member strength, D = dead load effect, and L = live load effect. The statistical values of the load and load effects were assembled from weight-in-motion programs, field tests, and other load meter information. 21. Ghosn, M. and F. Moses, NCHRP Report 406: Redundancy in Highway Bridge Superstructures, Transportation Research Board, National Research Council, Washington, D.C., 1998, 50 pp. In this report, Ghosn and Moses defined bridge redundancy as “the capability of bridge superstructure to continue to carry loads after the damage or the failure of one of its members.” They recognized that redundancy is related to system behavior rather than individual component behavior. The current bridge specifications, however, generally ignore the interaction between mem- g R D L= − − RF E R X A E R X A E R X Y A u i k u i k u i j k = ( )[ ] ( )[ ] − ( )[ ] , , , , RF E R X Y A E R X A u i j k u i k = ( )[ ] ( )[ ] , , , RF R X A R X A R X Y A R f X Y u i k u i k u i j k u i j = ( ) ( ) − ( ) = , , , , , , , , , , ,...A i j k mk( ) = 1 2 (ultimate strength of intact structure), RIF R X Y A R X A u i j k u i k = ( ) ( ) , , ,

bers and structural components in a bridge. To overcome the lack of interaction between members and components in current bridge design codes, Ghosn and Moses introduced system factors, related to system safety and redundancy, to be multiplied to nominal resistance of members. The multiplier factors could be used when evaluating the degree of redundancy of an existing bridge or when designing a new bridge. The load factors identified as LF1, LFu, LFf, and LFd could be calculated for any bridge configuration using a finite-element analysis. LF1 is expressed as the maximum number of AASHTO HS-20 trucks that the structure can carry before first mem- ber failure. LF1 could be calculated using linear elastic structural models and incrementing the load until the failure of the first member. LFu is the ultimate limit state and could be calculated by performing a nonlinear analysis of the structure under the effect of the dead load and two side-by-side AASHTO HS-20 trucks. LFu is then obtained by incrementing the truck loads until the system collapses. LFf is the structure capacity to resist large displacements and is expressed as the number of AASHTO HS-20 trucks that will cause a violation of the functionality limit state, which is chosen to be span length/100. Finally, the damage condition, LFd, is calculated by conducting a nonlinear analysis on the damaged structure using two side- by-side AASHTO HS-20 trucks. LFd is then obtained by incrementing the truck loads until the system collapses. To provide a reliability-based level of redundancy, relative reliability needs to be calculated. The values of βult, βmember, βfunct, βdamaged could be obtained using Equations 2, 3, 4, and 5 in NCHRP Report 406. It is important to note that an adequate level of redundancy is satisfied if obtained values of Δβu, Δβf, and Δβd are greater than or equal to 0.85, 0.25, and −2.70, respectively. For direct system redundancy approach, adequate load factor ratios (system reserve ratios) are required to satisfy a mini- mum level of redundancy. where The redundancy of the bridge system is then considered adequate if Ru, Rf, and Rd are greater than or equal to 1.30, 1.10, and 0.50, respectively. It is important to note that NCHRP Report 406 indicates that bridges that do not meet the required load factor ratios could still provide a high level of system safety. This could be checked by investigating if the capacity of the member meets or exceeds the capacity required by the specifications. 22. Lenox, T.A. and C.N. Kostem, “The Overloading Behavior of Damaged Steel Multigirder Bridges,” Fritz Engineering Laboratory Report No. 432.11, Lehigh University, Bethlehem, Pa., Mar. 1988. Lenox and Kostem (22) conducted a parametric analytical study of three multigirder bridge models. Every model had six par- allel girders and a span length different from the other models. The analysis revealed that after major damage has occurred in the exterior girder at the midspan, the load is redistributed mainly among the structural components in the vicinity of the dam- age. It was also noted that a significant amount of internal redundancy exists in simple-span steel highway bridges, resulting in a large increase in deformations and stresses at the vicinity of the exterior girder after it develops a sever damage. Bridge deck and cross bracing members played a major role in the redistribution of the load after the exterior girder is damaged. An insignificant response of the multigirder bridge was observed when the damage was only in the lower flange of the girder. However, a significant response was observed when half web crack was introduced in the exterior girder. 23. Daniels, J.H., W. Kim, and J.L. Wilson, NCHRP Report 319: Recommended Guidelines for Redundancy Design and Rating of Two-Girder Steel Bridges, Transportation Research Board, National Research Council, Washington, D.C., 1989, 148 pp. R LF LF R LF LF R LF LF u u f f d d = = = 1 1 1 Δ Δ Δ β β β β β β β β u f d = − = − = ult member funct member damaged member− β 74

75 Daniels et al. (23) provided guidelines for the design and rating of a redundant bracing system on new or existing two-girder steel bridges. They also investigated the after-fracture redundancy of simple span and continuous, composite and noncom- posite, steel two-girder highway bridges. The investigation was done using an analytical model in which a near full-depth frac- ture was assumed to occur at any position along the length of one of the two girders. The fracture was introduced in the ten- sion flange and in the full depth of the web (no fracture of compression flange). The bridge system used in the model consisted of top and bottom bracings (laterals) and diaphragms. The analysis concluded that significant redundancy could be achieved if redundant bracing systems (top and bottom later- als and diaphragms) are properly designed. Furthermore, if the bracing system is not originally designed for redundancy, the bridge system could still exhibit significant after-fracture redundancy if the bracing system is properly configured. Finally, there is a need for a new redundancy rating, which could be calculated by the allowable stress or load factor methods. 24. Chen, S.S., J.H. Daniels, and J.L. Wilson, “Computer Study of Redundancy of Single Span Welded Steel Two-Girder Bridge,” Report FHWA-PA-85-047+84-20, Federal Highway Administration, Washington, D.C., Mar. 1986, 72 pp. Chen et al. (24) investigated the response of a simple-span welded right two-girder bridge to a midspan fracture of one of the two main girders. The investigation included a three-dimensional model of the bridge to allow for the interaction between the structural components. The finite-element analyses confirmed the findings of many researchers, which is the critical role played by components and details in carrying the load after the fracture of one of the girders. For the bridge used in the study, under the dead load, the girder crack was followed by cracking and warping in the deck, failing of a fixed bearing, and buckling of several cross- frame horizontal members. Overall, a significant insight was gained on the structural behavior and the redistribution mecha- nism of the load after the through-depth fracture of one of the two girders at midspan. 25. “Final Report of the Bridge Safety Assurance Task Force to the New York State Commissioner of Transportation,” New York State Department of Transportation, John Kozak, Chairmen of the Bridge Safety Assurance Task Force, June 1995. The Bridge Safety Assurance Task Force was formed primarily in response to the fatal collapses of Connecticut’s Mianus River Bridge in 1983 and the New York State Thruway Schoharie Creek bridge collapse in 1987 as a result of scour. The task force included experts in various fields related to bridge engineering in the areas of hydraulics, river mechanics, concrete, and steel. The individuals contributing in the area of steel bridges were Dr. John W. Fisher and Dr. J. Hartley Daniels. The report evaluates conditions significantly affecting structural safety of New York bridges and recommends action to enhance identi- fication of vulnerable bridges and prioritization of corrective actions. Vulnerability of steel bridges was examined and a procedure to assess vulnerability, based on average daily truck traffic, member type, susceptibility to fatigue, redundancy, and other factors were incorporated into the assessment procedure. The result of the assessment was a ranking that could be used to compare the vulnerability of a given bridge to other bridges and to permit more effective use of funds when considering which bridges to retrofit, repair, or replace.