Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 47

ρ w
R M dy

Distortional forces due to
bending and curvature
Distortional forces due to
torsional load

P P /2 P /2 P /2 P /2

I dw ⋅ K dw

= +

Box girder, top view

2 3 4

Eccentric
loading

Bending
action

Torsional
action

1

y

I y

x

BEF, side view

P /2 P /2

1 2 3 4

K

=

+ +

Analogous to

Bending
action

Box girder BEF

(a)

Mixed
torsion

Distortion

End diaphragm ( ) 1 4 End support ( )

2

1 4

Internal diaphragm ( )
Distorsional warping constant, I dw

2 3 Interior support ( ) 3

Bending moment of inertia, I y

Frame stiffness, K dw Elastic foundation modulus, K

(b)

Figure 2.30 Distortion of the box girder and its analysis approach: (a) box due to eccen-
tric loading; (b) equivalent beam on elastic foundation analysis.

to simulate the action, proper mesh has to be established with the grillage
points subjected to continuity and equilibrium. If there is no diaphragm
or cross-bracing, the transverse elements are formed by the slab, and they
should be spaced with at least four elements between the dead load points
of contraflexure. If internal or external diaphragms exist, the mesh joints
should coincide with the locations of the diaphragms. The function of the
internal diaphragms is maintenance of the shape of the box and reduction
of distortion. The function of the external diaphragms is reduction of the
differential displacement between boxes. Figure 2.31 shows different types
of multicell deck and their mesh definitions with longitudinal lines along
their respective ribs.
If finite element is adopted for the analysis, the same principle is applied
as stated for the grillage analogy method. To obtain meaningful results,
at least two elements should be used for the vertical or inclined web and at
least two (maybe more, if the flange is wide) elements should be used for
the top and bottom flanges. Figure 2.32 shows an example of using finite
element modeling for a box girder bridge. More detailed coverage for steel
box girder bridge is in Chapter 8.

2.5.5 Curved bridge
Horizontally curved bridges are commonly used. It has often been used in
complex, multilevel interchanges, where the geometrics of a bridge struc-
ture are dictated by the roadway alignment.
There are two approximate methods that have been used to analyze
curved girder bridges. The first method, called V-Load method, is used
for curved I-girder bridges. The second method, called M/R method, is
used for curved box girder bridges (FHWA/University of Maryland 1990).