Fracture-Critical System Analysis for Steel Bridges (2018) / Chapter Skim
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From page 13... ...
13 This chapter summarizes the findings after the research methodology described in Section 2.2 was carried out. First, the development of an FEA methodology for the redundancy evaluation of typical steel bridges is discussed, as follows: • Description of the analysis procedures, techniques, and inputs required to construct finite element models to evaluate steel bridges for redundancy, in Section 3.1; • Discussion of reliability-based load models that characterize bridge loading conditions in the faulted condition, in Section 3.2; • Establishment of minimum performance requirements for steel bridges in the faulted condition, in Section 3.3; and • Calculation of the dynamic amplification of load caused by sudden failure of a steel tension member, in Section 3.4.
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From page 14... ...
14 • Ability to include material models that can be used to simulate nonlinear behavior of steel and reinforced concrete. Additionally, the analyst must be able to specify the density, material damping, and field-variable–dependent material properties.
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15 Explicit dynamic analysis is used when inertial effects need to be considered or when the problem becomes nonlinear and prevents convergence of an implicit analysis. It uses a central-difference time integration rule, in which the solution at the end of a time increment is computed based on the state of the system at the beginning of the time increment.
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16 For calculating the dynamic amplification factors caused by the fracture event, the following step for modeling sudden fracture -- continued from Steps 1 to 5 in Section 3.1.1.1 -- is carried out in the final explicit dynamic analysis: 6. Instantly delete the elements in the member under consideration.
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17 6. Change the moduli of elasticity of concrete and reinforcement to 3,600 ksi and 29,000 ksi, respectively.
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18 –5 –4 –3 –2 –1 0 1 –0.015 –0.01 –0.005 0 0.005 0.01 0.015 St re ss (k si) Strain (–)
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19 of tensile inelastic straining takes place at shared edges of slab segments poured and hardened at different stages. The no-sequence scenario shows large concentrations of tensile inelastic behavior in the concrete slab at locations over interior supports (negative-moment regions)
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20 No-Sequence Model One-Sequence Model Detailed Sequence Model Pier 8 Pier 9 Pier 10 Pier 11 Figure 9. Comparison of tension cracking in concrete slab of the Neville Island Bridge, viewed from top.
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21 However, larger differences in the longitudinal stress in the top flange was computed, as shown in Figure 14, Figure 15, and Figure 16 for Girder D, Girder E, and Girder F, respectively. In the case of the Hoan Bridge, the simplified pouring sequence scenario resulted in larger stress values in all spans, up to 2 ksi larger than the detailed sequence scenario.
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From page 22... ...
22 –20 –10 0 10 20 –1,000 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 Lo ng itu di na l N or m al S tr es s (k si ) Distance from Pier 5S (in.)
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23 is assumed to be poured and hardened at once (simplified pouring sequence scenario)
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24 3.1.2 Material Models The majority of the primary load carrying components in a bridge superstructure are made either of steel or of concrete. During this research, a linear elastic–Mises plastic relation with linear kinematic hardening and a specified failure strain for modeling steel components was used and is recommended.
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25 strength and two constants, one related to the cementitious material type (concrete, mortar, or paste) and another related to the type of aggregate and test method used.
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26 length of the truss elements was approximately equal to the length of the longest edge of the solid concrete elements. These truss elements were also embedded within the solid concrete elements.
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27 of the inelastic response of the shear stud group, as well as different expressions for the calculation of the initial stiffness, nominal tensile strength, and maximum cumulative tensile displacement. In general, concrete breakout strength is lower than the steel rupture strength or concrete pullout strength, hence becoming the governing failure mode.
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28 benchmarked against the full-scale experiments conducted by Neuman (2009)
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29 bolt. The bearing stiffness of the plate can be calculated as follows: ( )
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30 amplification factors, which are discussed in Section 3.2 and Section 3.4. Although analyses focused on the dynamic behavior of the structure were carried out to determine the dynamic amplification factor, the FEA methodology was developed so that its application did not require such complex analysis.
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31 as SRM would not be subjected to FCM hands-on inspections again. Additionally, since the calculated load factors are rounded to 1⁄20 (i.e., 0.05)
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32 3.2.2 Load Factors for Redundancy II Load Combination Once the required reliability level is established for the load combinations to be used in the analysis, the load factors can be calculated using the same procedures used in the development of those already included in the AASHTO LRFD BDS. For ease of understanding, the calculation of load factors for the Redundancy II load combination are explained first.
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33 Component Span(ft) Space (ft)
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34 Shear 3.30 3.94 1.57 3.86 3.95 0.49 4.27 3.95 2.57 4.53 3.95 0.12 4.83 3.95 1.50 2.53 4.01 2.27 3.15 4.01 1.52 3.73 4.01 1.68 3.84 4.01 0.72 4.15 4.00 1.98 2.16 3.81 3.88 2.48 3.81 0.45 2.86 3.82 0.36 3.02 3.81 2.51 3.32 3.81 0.22 1.87 3.98 0.76 2.33 3.98 0.56 2.71 3.98 1.08 2.83 3.98 0.85 3.05 3.96 0.57 30 60 90 120 200 2.30 4.00 2.19 2.72 4.01 0.90 2.99 4.02 0.43 3.21 4.01 0.81 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 4 6 8 10 12 3.36 3.90 4.36 4.49 4.69 2.66 3.23 3.66 3.85 4.06 2.04 2.53 2.92 3.11 3.32 1.92 2.37 2.71 2.89 3.07 2.32 2.74 3.02 3.22 3.37 3.33 1.88 0.95 2.02 0.99 3.07 5.00 2.41 1.80 0.29 2.28 5.68 1.89 2.14 2.93 0.01 2.73 1.66 0.07 2.04 0.53 0.88 0.57 1.14 0.45 1.16 3.99 3.88 3.93 3.85 3.95 4.01 3.92 3.95 4.08 3.98 4.08 3.96 3.79 3.81 3.71 3.82 3.95 4.00 4.02 3.95 3.98 4.09 4.05 4.04 4.04 4.02 0.80 Component Span(ft) Space (ft)
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From page 35... ...
35 where DC = dead load of structural components and nonstructural attachments, DW = dead load of wearing surfaces and utilities, LL = vehicular live load, and IM = dynamic load allowance. 3.2.3 Load Factors for Redundancy I Load Combination After the load factors of the Redundancy II load combination have been calculated, the load factors for the Redundancy I load combination can more easily be defined.
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36 reliability. To account for these benefits, the live load factor for bridges built to Section 12 of the AWS D1.5 was reduced from 0.90 to 0.85.
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37 intact components of the bridge in the faulted state. When positive flexure is being evaluated, the centroid of the truck component of the HL-93 live load model shall be positioned longitudinally coincident with the location of the primary member failure under consideration, with a proposed fixed axle spacing of 14 ft.
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38 distributed across the bridge is determined by the number of lanes multiplied by MPFstrength. The results for two, three, and four lanes loaded for the strength limit state are shown in Table 5.
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39 stress and strain and then to evaluate the overall strength of the system. Therefore, the acceptance criteria for strength presented below were developed with this in mind while relying on established limits currently contained in AASHTO specifications, where feasible.
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40 model in all load combinations, the displacements and reaction forces at support locations are calculated in the analysis. These should be taken as the factored demands that the substructure must be able to safely sustain.
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41 a deflection limit of L/50 after the failure of a primary steel tension member was deemed reasonable. A major advantage of ignoring live load ensures that designers will not attempt to strengthen the bridge to meet a deflection limit in the faulted state.
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42 limits on deflections that result in strengthening of a given structure to meet deflection limits and again, the unintended consequence of making it more difficult to detect the faulted condition. The proposed limit meets the objective of maximizing the likelihood that the deflection will be sufficiently large to alert the authorities or the motoring public.
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43 described in the AASHTO LRFD BDS for the Fatigue II load combination)
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44 were described in the reviewed literature. Because the constant amplitude fatigue limit for Category C is 10 ksi, actual in-service stress ranges rarely, if ever, will exceed this value.
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45 cumstance -- permitted to be considered capable of providing reliable redundant capacity in the faulted state. The criteria were established based on the work by Parr et al.
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