Bridge Superstructure Tolerance to Total and Differential Foundation Movements (2018)

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NCHRP Project 12-103 214 9 Framework for Estimating Maximum Tolerable Support Movement The following framework is provided to guide engineers in the refined evaluation of support movement(s). It is based on the approach used in this project and can be used as a basis for evaluating any structure under any loading condition and support movement scenario. Figure 9-1 provides a flowchart of this approach.

NCHRP Project 12-103 215 Figure 9-1 - Flowchart for refined evaluation of support movements. There are many approaches to FE modeling, simulation, and analysis. The approach instituted in this study is only one such approach. The method by which steps 1 through 4 are completed shall be left to the discretion of the engineer. The rating factor methodology is employed in this framework to evaluate a structure for any level of support movement. Using the rating factor approach described in Figure 9-1,

NCHRP Project 12-103 216 if the superstructure rates 1.0 or greater, then the engineer shall conclude the imposed level of support movement as tolerable. Otherwise, if the initial or retrofit design is to be adjusted, the superstructure must be re-evaluated for support movements. Re-evaluation is necessary after every change to the design as any change in stiffness has been found to have a significant effect on superstructure tolerance to support movements. If instead the maximum level of support movement is desired, the engineer shall impose the support movement with a maximum unit displacement and solve for the maximum tolerable support movement using the equation below (Equation 4-1 repeated from Section 4). This expression (and the one above) is based on superposition and thus assumes linear response. The tolerable support movement computed from Equation 9-1 will be in units of length (e.g. in.). As an example, in the case of a flexure limit state, the numerator would be in units of moment (e.g. kip-in) and the units of the denominator would be in units of moment per unit support movement (e.g. kip-in/in). For the expression in Figure 9-1, the rating factor (RF) is dimensionless, and the values in the numerator and denominator will be in similar units, dependent on the limit state and response being evaluated. This expression is formulated for each Strength and Service limit state shown in Table 1-3 using the force effects associated with dead load, super-imposed dead load, live load, and support movements computed using the 3D FE models described in Section 3. Equation 9-1 – Formula for calculation tolerable support movement. ܴܨ = ܴ߮௡ − ߛ஽௅(ܦܥ1 + ܦܥ2) − ߛ௅௅(ܮܮ)ܯݒݐ Where, RF = rating factor for tolerable support movement ϕRn = factored resistance γDL = load factor for dead load demands γLL = load factor for live load demands DC1 = initial dead load force effects DC2 = superimposed dead load force effects LL = live load force effects Mvt = force effects due to a unit support movement