Stability - Computational Analysis and Design of Bridge Structures - page 450

14.5 3D illuStratED ExaMplE with
linEar Buckling analySiS of a
StanDarD SiMplE arch riB
This example is to demonstrate the basic stability analysis—linear, or elastic,
buckling analysis. In this example, a prismatic single arch rib with a span
of 50 m is fixed at both ends. The geometry of the rib axis is a parabolic
curve with a chord height-to-span length ratio of 0.3. Moment inertia on
both in-plane and out of plane are equivalent. Both weight-equivalent cross-
sectional area and stiffness-equivalent cross-sectional area are the same too.
The material is concrete.
Figures 14.12 through 14.14 show the first three modes of linear
buckling analysis, respectively. The ratios of critical loads to the applied
loads, the structural weight, are 408.516, 1046.208, and 1259.367,
respectively. Table 14.1 shows the comparison between VBDS (Wang
and Fu 2005), a special-purpose bridge FEA package, and a theoretical
formula (Li 1996). Values in the table are converted from critical load
factors (λ).
Figure 14.12 The first mode of a simple arch bridge bulking, out of plane ( λ = 408.516).