Stability - Computational Analysis and Design of Bridge Structures - page 447

centerline. Not only the tension, the positive K σ but also the laterally sloped
geometry K L of the cables will enhance the lateral stiffness.
Again, the stability analysis of a long-span cable-stayed bridge can be
combined with its nonlinear analysis. The analysis of a long-span cable-
stayed bridge with a main span of 1088 m, however, shows that the stati-
cally geometrical nonlinear stability analysis is not sufficient. The total
tangential stiffness, with K L included, hardly reaches zero. This suggests
that aerodynamic stability analysis and the geometric plus material non-
linear analyses are required (Ren 1999). When material nonlinearity is
considered, a uniaxial representation of the bilinear elastic and perfectly
plastic steel constitutive law is employed. The von Mises yield criterion,
which is considered most suitable for structural steels, can be selected to
extrapolate a yield surface in three-dimensional (3D) principal stress space.
A full nonlinear stability analysis provides greater accuracy by incremen-
tally increasing load application until a structure becomes unstable. This
condition of instability is achieved when a small increase in the load level
causes a very large change in displacement. Nonlinear stability analysis is a
static method that accounts for material and geometric nonlinearities, load
perturbations, geometric imperfections, and gaps. Either a small destabiliz-
ing load or an initial imperfection is necessary to initiate the solution of a
desired buckling mode.
A nonlinear analysis requires incremental load steps in an explicit or
implicit manner. At the end of each increment, the structure geometry
changes and possibly the material is nonlinear or the material has yielded.
An explicit nonlinear analysis performs the incremental procedure, and
at the end of each increment updates the stiffness matrix based on the
geometry changes and material changes (if applicable). An implicit nonlin-
ear analysis does the same thing but uses Newton-Raphson iterations to
enforce equilibrium, which is the primary difference between the two types
of analyses. Either explicit or implicit nonlinear static analysis can be used.
However, for nonlinear stability analysis, the implicit method is preferred.
14.4 3D illuStratED ExaMplE with
linEar Buckling analySiS of a
pony truSS, pEnnSylvania
This example is to verify the hand calculation of a pony truss bridge
shown in Section 14.2.2 by eigenvalue buckling analysis. Eigenvalue buck-
ling analysis done by ANSYS predicts the theoretical buckling loads of
an ideal elastic structure by performing classical Euler buckling analysis.
Eigenvalues are computed for the given structure with the given boundary
conditions and loading. The cross section and the perspective view of the
bridge are shown in Figures 14.7 and 14.8, respectively.