Civil Engineering Reference
In-Depth Information
conditions can be applied to any of the displacement or rotation degrees of
freedom (6 degrees of freedom). Boundary conditions are treated as con-
straints during the eigenvalue buckling analysis. Therefore, the buckling
mode shapes are affected by these boundary conditions. The buckling
mode shapes of symmetric structures subjected to symmetric loadings
are either symmetric or antisymmetric. In such cases, it is more efficient
to use symmetry to reduce the finite element mesh of the model. Axisym-
metric structures subjected to compressive loading often collapse in non-
axisymmetric modes. Therefore, these structures must be modeled as a
whole. The loads prescribed in an eigenvalue buckling analysis can be con-
centrated nodal forces applied to the displacement degrees of freedom or
can be distributed loads applied to finite element faces. The load stiffness
can be of a significant effect on the critical buckling load. It is important
that the structure is not preloaded above the critical buckling load. During
an eigenvalue buckling analysis, the model's response is defined by its lin-
ear elastic stiffness in the original state. All nonlinear or inelastic material
properties are ignored during an eigenvalue buckling analysis. Any struc-
tural finite elements can be used in an eigenvaluebucklinganalysis.The
values of the eigenvalue load multiplier (buckling loads) will be printed
in the data files after the eigenvalue buckling analysis. The buckling mode
shapes can be visualized using the software. Any other information such as
values of stresses, strains, or displacements can be saved in files at the end of
the analysis. Further details regarding the eigenvalue buckling analysis can
be found in [
5.1
].
5.5.3 Materially and Geometrically Nonlinear Analyses
Materially nonlinear analysis of a structure is a general nonlinear analysis
step. The analysis can be also called as
load-displacement nonlinear material
analysis
. All required information regarding the behavior of bridges is pre-
dicted from the materially nonlinear analysis. The information comprised
the ultimate loads, failure modes, and load-displacement relationships as
well as any other required data that can be obtained from materially
nonlinear analysis. The initial overall and local geometric imperfections,
residual stresses, prestressing, and nonlinear stress-strain curves of the con-
struction material are included in the load-displacement nonlinear material
analysis. Since most, if not all, bridge components have nonlinear stress-
strain curves or linear-nonlinear stress-strain curves, therefore, most of
the general nonlinear analysis steps associated with bridges are materially
nonlinear analyses.
Search WWH ::
Custom Search