The girder system analysis uses either a grid model or a plate and eccentric beam finite element model.
Composite section properties in the grid model by default are used the entire length of the bridge for composite dead load and live load analysis. If composite and noncomposite regions are defined, the slab is ignored in the negative moment regions when determining member stiffnesses. Girder nodes are located at each girder and bracing connection. Horizontal curvature is used to determine lateral bending stresses. Horizontal support releases do not affect the grid model.
In the finite element model the slab is used the entire length and width of the bridge for analysis. Plate elements model the concrete slab, and eccentric beam elements model the steel girder. The eccentricity of the beam elements is used to account for composite behavior. There are three finite element mesh schemes available: (1) a low resolution model with beam and plate nodes at each bracing connection, (2) a medium resolution model with the same number of beam nodes as the low resolution model but with additional nodes off the girders for better plate element mesh symmetry, (3) a high resolution model with many more nodes both on and off the girders. Horizontal support releases only affect the finite element analysis.
Cross braces are converted to an equivalent beam element for the analysis both in the grid model and the finite element model (see Bracing Stiffness below.) After the analysis, cross braces are converted back to the configuration of members to determine bracing member forces. The governing combinations of maximum and concurrent shear and moments at each end of a brace are used separately as loading, where the top and bottom connections at that end have been released. Connections at the other end are assumed pinned. Shear is distributed evenly to the released connection points. Moment is resolved into a force couple loading the release points horizontally. Separate analyses are carried out for noncomposite dead load, composite dead load, and live load effects. Determinate truss analysis is used to determine forces in the diagonals and chords of cross bracing. Diaphragm connections are assumed to transmit moment.
Each cross brace is converted to an equivalent prismatic beam by releasing one end of the bracing (using the connection plate as a member of the truss) and placing a roller under this end, which is then free to rotate. A unit moment is applied to the released end as a force couple applied horizontally to the top and bottom of the truss. The rotation of the released end is obtained by determining horizontal displacements of the top and bottom nodes. The moment of inertia, I, for the equivalent beam then is determined using the expression for rotation due to a unit moment, L/4EI. Torsional stiffness is obtained simply by adding the torsional stiffnesses, J, of chords and diagonals intersecting an interior vertical section of the truss.
The girder system live load analysis involves a separate analysis for a unit load at each girder tenth point. Influence surfaces are constructed from the unit load analyses for girder shear, moment, torque, and defections at each tenth point, as well as for reactions and bracing forces.
Trucks are positioned laterally in each lane for maximum effect. If the design speed and superelevation are defined, centrifugal force effects are included in the influence surface loading process by applying unbalanced wheel loads (see USS HIGHWAY STRUCTURES DESIGN HANDBOOK, Chapter 11/6.) The governing effect of either including or not including centrifugal force effects is determined. Centrifugal effects are not accounted for in horizontal reactions. Instead of direct lane loading, the user can specify wheel distribution factors in which case influence surfaces are sliced along each girder, producing influence lines.
Uniform AASHTO lane loading, treated as a line loading which is laterally located midway between wheels, is applied for maximum effect to each lane.
Lanes either can be fixed in place or transversely floated. In the latter case, the set of lanes is translated laterally and realigned to maximize the load effects being determined. Governing lane combinations determine the live load envelopes.
Live load analysis results are stored for subsequent girder and bracing design runs or rating output generation.
In Girder System Design Projects, a preliminary girder system analysis must be run to establish a set of preliminary member forces for girder and bracing design generation. By default a generic set of relative girder and bracing section properties are used for the preliminary analysis. However, preliminary girder and bracing section properties can be specified to achieve greater precision in the preliminary analysis.
As girder designs are generated the resulting girder stiffnesses automatically are stored for reanalysis. If the grid model is used for reanalysis, the St. Venant torsion stiffness for the girder is calculated using the steel cross section and one-half of the transformed slab. There are several options available for modeling composite behavior for a grid model (see Analysis Options Input Reference.) If a finite element model is used for reanalysis, the St. Venant torsion stiffness for the girder is calculated from the steel cross section alone since the slab torsional stiffness is accounted for in the plate elements. Until the bracing designs are generated or bracing section properties are specified, braces have the following default section properties: flexural moment of inertia of 1000 in4 (4.16 x 108 mm4) and torsional stiffness of 5 in4 (2.08 x 108 mm4. ) When bracing designs are generated the resulting bracing stiffnesses automatically are stored for reanalysis.
A Strudl format input file is generated when a girder system nodal output option (see DEAD LOAD 1 NODAL OUTPUT, DEAD LOAD 2 NODAL OUTPUT) is selected and influence surface values can be listed (see DISPLAY INFLUENCE SURFACES, INFGDR) so that the user can independently verify girder system analysis output. Furthermore, trucks can be placed at particular locations (see GPLACE, LPLACE, TPLACE, TLANES, TRUCK HEADING LEFT, and TRUCK HEADING RIGHT) and corresponding Strudl format input generated for comparison.