Curved concrete bridges - Computational Analysis and Design of Bridge Structures - page 177

in practice. Plane frame analysis is acceptable for curved bridges that have
a central angle less than 12°. For bridges that have a central angle greater
than 12°, curve geometry should be considered in the analysis model, and
3D spine frame analysis is required when a curved bridge is modeled as a
series of straight (or curved) frame elements in the centerline. Otherwise,
specialized curved beam elements are preferred. On the other hand, the 3D
FEAs are less vulnerable to applicability and modeling scope. Although this
analysis is still an approximate method, a closer to actual bridge behavior
can be generated by creating a more complex bridge model. With today's
advanced technology with mesh-generating power, a bridge-designated
FEA program can build a finite element bridge model to ensure the correct-
ness of the model, and it is more frequently used in practice.
6.2.1 Modeling of curved concrete bridges
Curved concrete bridges, based on their level of required accuracy can be
modeled into different types, from spine model to grid model to 3D finite
element model. * Also, based on their emphases, bridges can be analyzed as
decoupled super- or substructural model or a global bridge model. A global
bridge, which includes the entire bridge with all frames and connecting
structure, may be needed for certain circumstances, especially for earth-
quake analysis as discussed in Chapter 17. The three types of modeling are
described briefly as follows:
1. Spine model. Spine models as shown in Figure 6.5a simplify the whole
cross section, no matter single- or multicell boxes. The 3D frame ele-
ment considers six degrees of freedom at both ends of the element and
is modeled at their neutral axis. In this model, prestressing can be
considered as equivalent loads with axial, vertical, and translational
equivalent forces, or prestress tendons can even be included in the
model as truss elements, as described in Chapter 5. Figure 6.6a demon-
strates a single-box sitting on two bearings by connecting the neutral
axis by rigid element. Different types of bearings, such as polytetraflu-
oroethylene (PTFE), stainless steel sliders, rocker bearings, or elasto-
meric bearings, may be used, and they should be modeled accordingly
with directional restraints or springs. For bearing-supported connec-
tions, only up to three translational degrees of freedom are restrained,
but the rotational degrees of freedom are free. Three 3D rigid truss
elements can be used to simulate the three translational restraints.
Figure 6.6b, adopted from Priestley et al. (1996), illustrates a typical
* 3D FEM model in this chapter refers to a finite element model in 3D that differs from spine
and grillage models. Usually a 3D finite element model contains plane shell elements and
other types of elements.