Bridge Superstructure Tolerance to Total and Differential Foundation Movements (2018) / Chapter Skim
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NCHRP Project 12-103 14 whether the current guidance (regardless of its initial intent) could accurately reflect tolerable TD support movements.
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NCHRP Project 12-103 15 approaches, the use of bins ensures a more uniform coverage of the parameter space (McKay et al.
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NCHRP Project 12-103 16 of girder spaces, which is then multiplied by the actual girder spacing to obtain the adjusted bridge width.
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NCHRP Project 12-103 17 Table 3-3 - Design constants for steel and PS concrete bridges. Design Constant Value Concrete Density 150 pcf Deck Concrete Compressive Strength 4 ksi Barrier Height 27 inches Barrier Width 12 inches Deck Thickness 8 inches 3.2 Automated LRFD (Task 2.1.2)
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NCHRP Project 12-103 18 Dead load demands for PS concrete multi-girder bridges were computed in the same manner as steel girder bridges, with one exception; for multiple-span continuous PS concrete bridges, the initial dead load demands were computed with the spans acting individually (i.e., simple spans) while the superimposed dead load and live load demands were computed with the spans acting continuously.
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NCHRP Project 12-103 19 The scalar, or "objective" function, within the member-sizing algorithm was taken as the area of the steel section. In the same manner that the typical designer may attempt to find the most economical section that satisfies all constraints set by AASHTO LRFD, the fmincon algorithm attempts to find the combination of variables (i.e.
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NCHRP Project 12-103 20 Proportioning Limits D୵ t୵ ≤ 150 b 2t ≤ 12 b ≥ D୵ 6 t ≥ 1.1 ∗ t୵ 0.1 ≤ I୷ୡI୷୲ ≤ 1 6.10.2 Web Thickness Limit t୵ ≥ 0.3125" 6.7.3 Strength I Positive Flexure M୳ ≤ M୬ if ଶୈౙ୲౭ ≤ 3.76ට ౯ fୡ, ୲ ≤ F୬ if ଶୈౙ୲౭ ≥ 3.76ට ౯ 6.10.6 Strength I Negative Flexure fୡ ≤ F୬ 6.10.8 Service II Positive Flexure fୡ, ୲ ≤ 0.95 ∗ F୷ 6.10.4 Service II Negative Flexure fୡ, ୲ ≤ 0.80 ∗ F୷ 6.10.4 Shear V୳ ≤ V୬ 6.10.9 Fatigue I γ(∆f)
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NCHRP Project 12-103 21 Where, L = span length D୧୰ୢୣ୰ = depth of the steel section Dୱୣୡ୲୧୭୬ = depth of the composite section D୮ = depth of compression at the plastic moment for the composite section D୵ = depth of the web Dୡ = depth of the web in compression t୵ = thickness of the web b = flange width t = flange thickness I୷ୡ , I୷୲ = moment of inertia of the compression and tension flanges, respectively E = Young's modulus of elasticity F୷ = Steel yield strength M୳ = factored ultimate moment demand M୬ = nominal moment capacity fୡ, ୲ = compression/tension stress in the flange F୬ = nominal compressive/tensile stress capacity V୳ = factored ultimate shear demand V୬ = nominal shear capacity (∆F) ୌ = fatigue stress limit γ(∆f)
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NCHRP Project 12-103 22 PCBT 61 125 PCBT 69 135 PCBT 77 145 PCBT 85 150 PCBT 93 155 An iterative approach was used in selecting the number of pre-stressing strands as well as the concrete compressive strength. An initial minimum compressive strength of 4 ksi and a minimum number of eight pre-stressing strands was assigned.
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NCHRP Project 12-103 23 Figure 3-3 - Framework for sizing of PS concrete girders. Table 3-6 - Constraints used for PS concrete girder sizing, adopted from AASHTO LRFD.
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NCHRP Project 12-103 24 transient loads (Service I) : ௌ݂௩ଵ < 0.6 ∗ ݂′ Compressive stress limit for live load plus one-half the sum of the effective pre-stress and permanent loads: ݂ଵ ଶ(ௌା)
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NCHRP Project 12-103 25 3.2.4 Software Validation Validation of the member-sizing processes described above was a critical task of the project. In order to draw reliable conclusions about tolerable support movements, the process adopted must be capable of producing member sizes that are consistent with all the requirements of AASHTO LRFD without additional and/or arbitrary conservatism.
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NCHRP Project 12-103 26 In addition to the "one-to-one" validation approach, the UD research personnel performed an independent, line-by-line auditing of the source code for the automated member-sizing software to validate all components of the software. This audit was conducted to ensure that there were no typographical or syntax errors and all appropriate equations were present and being calculated properly.
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NCHRP Project 12-103 27 Figure 3-4 - Step-by-step approach to automated FE model construction. 3.3.1 Model Form A wide range of modeling techniques are available to simulate the behavior of common multi-girder bridges.
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NCHRP Project 12-103 28 Figure 3-5 - Schematic representation of the element-level model used for simulating a typical multi-girder structure (Masceri 2015)
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NCHRP Project 12-103 29 Figure 3-6 - Typical girder-cross frame connection (Masceri 2015)
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