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20 HNTB, as part of Milwaukee Transportation Partners, used The tie girder was modeled using elastic beam elements. these recommendations in a redundancy analysis for twin Elastic analysis is always conservative, even when used curved box girders designed for the Marquette Interchange with inelastic cross-section capacity, provided the sections in Wisconsin to demonstrate to FHWA that waiving the are sufficiently ductile. The analysis involved a 14-ft (4.2-m)- fracture-critical inspection requirements was justified (49). long segment of the tie girder representing a fractured resid- The boxes were going to be fabricated as FCMs anyway. ual section. The centroid of the C-shaped residual section is (Recall previously in this chapter that the fabrication part not collinear with the centroid of the uncracked tie girder, of the additional cost of FCMs is relatively small compared creating some additional bending moment. The capacity of with the in-service inspection part.) the residual section is then compared with the elastic moments from this model with the full-factored AASHTO A three-dimensional shell element model was used for LRFD Specifications HL-93 load and impact [1.25 DC + elastic incremental analyses, manually updating the mesh 1.50 DW + 1.30 (LL+I)]. Although no dynamic amplifica- to account for nonlinear effects. The reserve capacity of the tion effects were included, the Strength I factored loading is undamaged bridge was found to be 4.9 times HS-25 side-by- very conservative and would amount to a large multiple of side trucks for the pier section of the outside box and 3.4 times HS-20 trucks. HS-25 side-by-side trucks for the midspan section of the outside box. The residual capacity of the damaged midspan The capacity of the cross section is obtained from a model section was found to be 3.35 times HS-25 side-by-side trucks, that relates moment to curvature and strain. Nominal cross- above the 0.5 times the original reserve capacity recommended section strains of less than 1%, approximately six times the by Ghosn and Moses (34). yield strain of the HPS 70W steel, were considered accept- able. This level of allowable nominal strain allows a margin A dynamic amplification factor of 1.8 was conservatively for localized concentrated strains near holes and other dis- estimated using a single-degree-of-freedom impact model and continuities, and was supported by nonlinear finite-element assuming 5% of critical damping. Based on this, it was deter- analysis and testing of tension and flexural members made mined that the structure might have to withstand dynamic from similar HPS 70W at the University of Minnesota (52,53). stresses that are equivalent to 2.68 times HS-25 side-by- The residual cross section; that is, a cross section with either side trucks in addition to the static dead load effect. (The a web or a flange missing, was shown to be able to continue 2.68 level included the anticipated dynamic part of the dead to carry the load after such an event. Therefore, the tie girder load and both the static and dynamic part of one set of HS-25 was shown to meet the definition of redundant. trucks as the live load.) Because the residual capacity was greater than 2.68, the bridge is considered safe for the tem- This same type of analysis is being used to evaluate older porary dynamic loading. structures, as well to better direct resources for maintenance and replacement; for example, if a bridge is not really fracture- Lai (50) developed a three-dimensional finite-element critical then it may not be necessary to replace it as soon. For model and used a static incremental study to determine the example, as part of a study being conducted on the I-35W truss degree of redundancy of a tied arch bridge. He found that after bridge in Minneapolis, Minnesota, complex three-dimensional the fracture of the one of the ties, the structure was capable finite-element models of the bridge are being developed. of carrying its own weight plus 1.3 times HS-20 truck load- Fracture-critical members are removed from the model and ing without catastrophic collapse. the resulting redistribution of loads accurately is being studied. Adequacy of connections, individual components, and over- Michael Baker Jr., performed an analysis for the proposed all stability are being assessed. Blennerhassett Tied Arch Bridge in West Virginia (51). The tie girder section is a bolted built-up box section as shown in PRESENT CLASSIFICATION OF STEEL BRIDGE Figure 10b. Because the section is a bolted built-up section, SUPERSTRUCTURES AS FRACTURE-CRITICAL it has internal redundancy as discussed previously in this chapter. In this case, a fatigue crack, fracture, corrosion fail- Common assumptions that fractures in certain superstructure ure, ductile rupture, or other failure of any one of the four plates types will lead to collapse may be too simplistic, as shown by cannot propagate directly into any of the other three plates. the bridges traditionally classified as FCBs that did not col- lapse, as discussed earlier in this chapter. The designer justified using the inelastic capacity of the residual cross section because AASHTO LRFD Specifica- Table 1 is a chart assembled by the California DOT (Cal- tions Articles 4.5.2.1 and 4.5.2.3 permit inelastic response trans) showing the varying definitions of different superstruc- for extreme events, and the fracture of one of the plates in ture types as "fracture-critical" in four related documents. the cross section was considered an extreme event (51). The There appears to be substantial disagreement, as was also analysis of the Blennerhassett Bridge did not include the found in the survey conducted as part of this project (see chap- effect of plastic redistribution of forces, which, if included, ter three). Note that only the book (in the left-hand column) indicate greater capacity. considers two-box-girder systems to be FCBs. In the case

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TABLE 1 VARIOUS DEFINITIONS OF COMMON FRACTURE-CRITICAL BRIDGE SUPERSTRUCTURES Manual for Condition Evaluation and Bridge Inspection and Structural Inspection of Fracture Critical Bridge Bridge Inspectors Refere nce Manual Load and Resistance Factor Rating of Analysis (27) Members, Report FHWA-IP-86-26 (28) (29) Highway Bridges (3) Two-girder system (simple and One- or two-girder systems, including single Two-girder systems (single span and end span of Suspended span with two girders continuous span) boxes with welding continuous span units) Simple span two-girder bridge with Suspended span with pin and With fix hanger suspended span welded partial length cover plates on hanger system With suspended span the bottom flange Suspended span Suspended spans with two girders Welded plate girders Continuous span two-girder system Welded plate girder Riveted or bolted plate girders with cantilever and suspension link Riveted or bolted plate girder arrangement and welded partial length cover plates Simple span two-girder system with lateral bracing connected to horizontal gusset plates that are attached to webs Truss system (simple and continuous Two-truss systems Truss system (simple and continuous spans) Simple span truss with two eyebars or span) Eyebar truss single member between panel points Eyebar truss Welded truss Welded truss Truss with suspended span Riveted truss Riveted truss Three deck truss with pin and hanger assembly Suspension bridge Suspension systems with two eyebar Suspension bridge Bar chain suspension bridge with two Eyebar chain components Eyebar chain eyebars per panel Cable Cable (continues) 21

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22 TABLE 1 (Continued ) Tie arch Tie Arch Welded tie arches with box shape tie girder Welded tie box girder Welded tie arches Two welded tie box girder Riveted tie box girder Two riveted tie box girder Steel pier cap Steel pier caps and cross girders Steel pier cap Single welded I-girder or box girder Welded box or plate girder Welded box or plate girder pier cap with bridge girders and Riveted box or plate girder Riveted plate girder stringers attached by welding Two column steel bent Longitudinal box beam Single boxes with welding Longitudinal box beam Simple span single welded box girders Single welded box Single welded box with details such as termination of Single riveted box Single riveted box longitudinal stiffeners or gusset plate Anchor for cable stayed bridge Pin and hanger connections when used Pin and hanger connections on two- or three- in suspended span configuration in girder systems nonredundant systems Two or less box girders Three or more box girders if spacing is large (should be determined by structural engineer) Courtesy: Tom Harrington, Caltrans.

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23 of the AASHTO Manual for Condition Evaluation and Load support the full dead and appropriate live load after sustaining a and Resistance Factor Rating (LRFR) of Highway Bridges (3) complete fracture of the flange at any point. [identical to the predecessor Manual for Condition Evalua- tion of Bridges (54)] and the Bridge Inspectors Reference The commentary of this section states that: Manual (29), only welded tie members for arches or single box girders are considered FCMs, whereas riveted or bolted There may be exceptions where box flanges of single-box sections subject to tension need not be considered fracture-critical. For built-up tie members or single box girders, such as those example, continuously braced top flanges in regions of nega- shown in Figure 10, would not be FCMs. This would appear tive flexure where there is adequate deck reinforcing to act as to be giving credit to the internal redundancy of the bolted or a top flange in such cases, adequate shear connection must also be provided. riveted built-up members (but these manuals note elsewhere that internal redundancy should be neglected). The section was recently amended to include the following: In Table 1, not all two-I-girder bridges are considered Unless adequate strength and stability of a damaged structure can FCBs in some of the documents. The LRFR Manual and the be verified by refined analysis, in cross sections comprised of two reference manual include all two-I-girder bridges as FCBs. box sections, only the bottom flanges in the positive moment However, in Inspection of Fracture Critical Bridge Members region should be designated fracture-critical. Where cross sections (28), continuous two-girder bridges are not considered frac- contain more than two box girder sections, all of the tension flanges should be considered non-fracture-critical. ture-critical except for the end span. This FHWA report gives credit to the structural redundancy of the continuous spans. Therefore, the redundancy of two box or tub girders is some- times even in question. Twin tub girders would be expected to Unfortunately, the AASHTO LRFD Bridge Design Speci- perform even better than twin I-girders owing to the torsional fications are not clear about what types of superstructures are capacity of the intact tub girder and the alternate load paths to be classified as FCBs. The fatigue and fracture limit state available within each tub girder. Unfortunately, this built-in requirements are specified in Article 6.10.5. Special provi- redundancy shown by these structures is not explicitly rec- sions for box sections are included in Section 6.11.5, which ognized in the LRFD Specifications. As will be discussed in also states that: chapter three, the results of the survey revealed that different For single box sections, box flanges in tension shall be consid- agencies classify tub girders differently when determining if ered fracture-critical, unless analysis shows that the section can the bridge is fracture-critical or not.