Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 46

approximation of the beam model by using the effective width, live load dis-
tribution factors, and influence lines. There are several examples in Chapter
4 for RC beam bridge, Chapter 5 for PC beam bridge, and Chapter 7 for
steel I-girder bridge using this method.
There are several conditions to be met for a beam-slab bridge, and they
are defined in the AASHTO LRFD Specifications (2013) as
• Width of the bridge is constant.
• Number of beams is not less than four.
• Beams are parallel and have approximately the same stiffness.
• Roadway part of the overhang does not exceed 1 m (3 ft).
• Curvature in plane is less than the limit speciied in the AASHTO
LRFD Specifications (2013).
• Cross section is consistent with one of the cross-sections shown in the
AASHTO LRFD Specifications (2013).
If earlier conditions are violated, the refined methods, such as grillage anal-
ogy or FEM, are recommended. If the grillage analogy is used, the same
procedures defined for beam model can be used for each longitudinal beam,
and the transverse stiffnesses, D y and D yx , for the solid slab, as defined in
Section 2.4.2, can be used for the transverse beam element. If more detailed
information is required, finite element is a practical method. When applying
finite element, however, it has to be cautious that mesh size, coordinates,
loading directions, and boundary conditions affect on getting good results.
2.5.4 Cellular/box girder bridge
The beam model of this type can be built just like the beam-slab bridge
with the effective widths defined for each web. For segmental concrete box
and single-cell cast-in-place box beams, effective width is defined more
elaborately. As defined in the AASHTO LRFD Specifications (2013), a
beam model can be used as an approximate method with appropriate effec-
tive width and distribution factor, as mentioned in Section 2.2.
One of the differences between the detached box bridge and other girder-
type bridges is distortion of the box due to eccentric loading (Figure 2.30a);
the effect can be substantial for flexible section, such as steel. The EBEF
(equivalent beam on elastic foundation) approach (Figure 2.30b) provides
good approximation of the moments and stresses due to distortion and
warping around the box section (Heins and Hall 1981). If distortion and
warping are predominant, use of a more refined model, such as 3D FEM
model, is suggested.
For a cellular deck, where the cells are either attached or detached, the
principal modes of deformation are due to longitudinal bending, transverse
bending, torsion, and distortion. If grillage analogy method is adopted,