Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 41

2.5 DIFFERENT TYPES OF BRIDGES WITH THEIR
SELECTED MATHEMATICAL MODELING
If bridge structures need to be mathematically modeled, any piece-wise
approximation needs to be established first. An approximate solution is
reached by subdividing the structure into regions of interest. Substructure
and superstructure can be decoupled into two different analyses if they are
not constructed integrally.
Methods of analysis of highway bridges range from the simplified beam
model with live load distribution factors defined by a design specification
to the complicated 3D finite element model with influence surface loading.
The simplified beam model, with the newly developed distribution factor
(AASHTO 2013), is supposed to close the gap between these two extremes,
but it is still on the conservative side. Unless a more accurate method is
needed for rating or posting, the AASHTO method is still the most popular
method used in design of bridges.
As for the refined analysis, several methods have been mentioned in
Section 2.4. Among the methods, grillage analogy method is the most popu-
lar and 3D generic finite element is the most detailed. Comparing these two
methods, there are two important differences mentioned by Jategaonkar
et al. (1985), which are briefly discussed here:
1. Conservative/nonconservative results . The 3D generic finite element
analysis is an approximation to the exact solution. It can be shown
that as the number of finite elements in the model increases, provided
that a conforming type of elements is used, the convergence to the
exact solution is from below and the solution obtained from it is lower
bound to deflection and stresses, which is not conservative. A grillage
analysis, on the other hand, gives a theoretical solution based on the
assumption of the grillage model and is not so critical of the mesh size.
2. Accuracy . The 3D generic finite element analysis can refine the mesh
to obtain the local stress near the critical location, such as holes or
sharp turns, or heavily loaded location, such as the position of the
concentrated load. Grillage analysis can give accurate analysis results
in terms of overall moments and shears (and thus the overall stresses)
but not local stresses . In such cases, local stresses can be obtained by
handbooks, such as design aids for concentration factor, or closed form
solution, such as Westergaard method for deck bending in Section 2.1.
With this in mind, several mathematical models are suggested for different
types of bridges, and they are listed in the following sections.
When modeling and analyzing a bridge, it should be noted that 3D model-
ing with influence surface live loading may produce more accurate results for
a middle- or short-span bridge than a long-span bridge such as cable-stayed