Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 23

2.3 APPROXIMATE ANALYSIS METHODS

2.3.1 Plane frame analysis method
For the approximate analysis method (or so-called simplified method), a
longitudinal girder, or a strip of unit width as in the case of a slab bridge,
is isolated from the rest of the bridge and can be treated as a 1D beam or a
plane frame structure in general.
For long-span bridges, the whole bridge may be considered as a 1D
beam model. For straight multigirder bridges, this simplified method can
also be adopted for determining the controlling force and longitudinal
moments. A girder, plus its associated portion (effective width) of the slab,
is subjected to dead and live loads where dead loads can be approximated
by their tributary. However, live loads have to be maximized by loads'
lateral position and girder influence lines, which are called live load enve-
lopes. A study was made and summarized in the AASHTO load and resis-
tance factor design (LRFD) code (2013) as live load distribution factors.
Live loading results of one lane of design vehicles and/or lane load must be
multiplied by live load distribution factors to consider the lateral distribu-
tion of live loads. Usually different specifications have different calcula-
tion methods for live load distribution factors. Some may have the same
procedures. For example, AASHTO LRFD code (2013) and Ontario code
(OHBDC 1991) are using the similar approach.
Bridge deck —It is structurally continuous in the orthogonal directions
on the plane. The applied load on the deck will have 2D distributions of
shear forces, moments, and torques. If 2D distribution is considered, it is
definitely more complex than the one modeled as a 1D continuous beam.
In a refined analysis method, the transverse flexural stresses on the slab
can be found from the computer results. However, if a simplified method
is used, the transverse flexural stresses have to be checked separately. To
check the transverse flexural stresses on the bridge slab, Westergaard equa-
tions are always referenced.
In AASHTO LRFD Specifications (2013), width of the equivalent strip,
as shown in Figure 2.8, is taken as specified. Unlike fully and partially
filled grids, where live load moments may be determined by an empiri-
cal formula, the strip of concrete deck slab shall be treated as continuous
beams or simply supported beams between girders with dual wheels of
design truck applied.
The following equivalent strip width for concrete deck (Equations 2.1a
and 2.1b) is from AASHTO LRFD Specifications. It is a modified
Westergaard equation in SI units for calculating transverse flexural stresses
between girders.

660 0 55

(2.1a)

+ → = M E : + . S