The search for optimal bridge girder designs is carried out by a computational algorithm that satisfies the design constraints while obtaining a highly efficient balance of values for the design variables. Constraints on the design are all those appearing in the relevant sections of the 17th Edition of the AASHTO STANDARD SPECIFICATION FOR HIGHWAY BRIDGES for Allowable Stress Design (ASD) and Load Factor Design (LFD) or the 6th Edition of the AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS for Load and Resistance Factor Design (LRFD). For curved girders designed under ASD or LFD, all the relevant constraints appearing in the 1993 GUIDE SPECIFICATION FOR HORIZONTALLY CURVED BRIDGES for ASD, and either (by user’s choice) the 1993 or the 2003 GUIDE SPECIFICATION FOR HORIZONTALLY CURVED BRIDGES for LFD, also are satisfied. See Appendix B for references to these constraints.
The problem solved in order to obtain designs by optimization methods is:
Minimize F(X)
Subject to:
G1(X) < 0
G2(X) < 0
.
.
.
Gn(X) < 0
where F(X) expresses the weight of the girder.
The vector of unknowns, X, represents girder plate dimension and transverse stiffener spacings. The design constraints G(X) are the relevant AASHTO constraints from the chosen specification (ASD, LFD, or LRFD.)
For continuous composite girders the problem is amplified when the slab, being in tension, is not considered effective in negative moment regions for composite dead load and live load analysis. The difference in moment of inertia of positive moment and negative moment regions normally is significant, yet the inflection points between those regions are not known until the analysis is completed. Also, inflection points are different for dead loads than for each positioning of the live loads. Composite behavior can be modeled in several ways (see Analysis Options Input Reference.)
Because of the differences in inflection point locations corresponding to maximum and minimum live load effects, the slab by default in included in all section properties when determining influence lines. Composite and noncomposite regions can be defined for composite dead and live load analysis, except when using the finite element model in a girder system analysis.
The user can adjust the design to reflect practical considerations after a girder design is generated. For example, by default the minimum required flange thicknesses are generated at tenth points to show that section is required at these points. It is left to the user to modify flange dimensions and splice locations to meet practical considerations. Alternatively, flange splice locations alternatively can be specified prior to generating a girder design.
Smooth and rapid convergence toward an optimal design often is experienced. But occasionally a computational oscillation occurs during the search that inhibits convergence. Typically, fixing more design variables will help induce convergence.
Occasionally a mathematical difficulty arises, because of the highly nonlinear nature of the process, that precludes convergence to an optimal design. In such a case a message announcing nature of the difficulty suggests that the user adjust the range limits for certain variables. Girder dimensions are stored in girder input for subsequent modification and reanalysis.