Approximate and refined analysis methods - Computational Analysis and Design of Bridge Structures - page 42

or suspension bridge. When nonlinear effects are of concern, material non-
linear effect may play an important role for a middle- or short-span bridge,
whereas geometric nonlinear effect may be essential for a long-span bridge.
As modern modeling technique and analysis tools are widely available, 3D
modeling with influence surface loading is always encouraged. For a long-
span bridge, geometric nonlinear analysis should be considered in most cases.

2.5.1 Beam bridge and rigid frame bridge
To simplify the analysis, a beam-type bridge can be simply modeled by 2D
beam elements, and a rigid frame-type bridge can be modeled by 2D frame
elements. With this simple model and quick turnout, the model can be used
to analyze construction staging (Figure 2.24), thermal loading due to differ-
ential temperature (Figure 2.25), prestressing loading as equivalent applying
forces (Figure 2.26), and loading due to support movement (moment redis-
tribution in Figure 2.27b for nonsettlement case versus Figure 2.27c for dif-
ferential settlement case). Bridge with different soil conditions to simulate the
support movement (Figure 2.28a) can be modeled as a three-spring founda-
tion (Figure 2.28b). A frame structure with soil springs and their effects are
shown in Figure 2.29, where the three-spring constants can be represented by

0 5 .

25
1

GA

Vertical spring : K =

z

( − ν )

(2.11)

K G A

0 5 .

Horizontal spring : = 2 ( 1 + ν)

x

GZ

2 5
1

.

Rock spring: K =

zr

( − ν )

Moment

(a)

Moment

(b)

Figure 2.24 (a, b) Bridge construction staging.