Civil Engineering Reference
In-Depth Information
loss occurs through plastic or viscoelastic phenomena as well as from friction
at the interfaces between the matrix and the reinforcement. Still, larger
material damping is exhibited by thermoplastics. Mechanical dampers
may be added to models to introduce damping forces to the system. In gen-
eral, it is difficult to quantify the source of a system's damping. It usually
comes from several sources simultaneously, for example, from energy loss
during hysteretic loading, viscoelastic material properties, and external joint
friction.
Four categories of damping sources are available in ABAQUS [1.29]
comprising material and element damping, global damping, modal damping,
and damping associated with time integration. Material and element damp-
ing specifies damping as part of a material definition that is assigned to a
model. In addition, the software has elements such as dashpots, springs with
their complex stiffness matrix, and connectors that serve as dampers, all with
viscous and structural damping factors. Viscous damping can be included in
mass, beam, pipe, and shell elements with general section properties. Global
damping can be used in situations where material or element damping is not
appropriate or sufficient. Modelers can apply abstract damping factors to an
entire model using global damping. ABAQUS allows modelers to specify
global damping factors for both viscous damping (Rayleigh damping) and
structural damping (imaginary stiffness matrix). Modal damping applies only
to mode-based linear dynamic analyses. This technique allows modelers to
apply damping directly to the modes of the system. By definition, modal
damping contributes only diagonal entries to the modal system of equations.
Finally, damping associated with time integration, which results from
marching through a simulation with a finite time increment size. This type
of damping applies only to analyses using direct time integration. ABAQUS
also applies damping to a linear dynamic system in two forms, which are
velocity proportional viscous damping and displacement proportional
structural damping, which is for use in frequency domain dynamics. An
additional type of damping known as composite damping serves as a means
to calculate a model average critical damping with the material density as the
weight factor and is intended for use in mode-based dynamics.
5.6.2 Thermal (Heat Transfer) and Thermal-Stress Analyses
5.6.2.1 General
Steel and steel-concrete composite bridges may be analyzed to evaluate
temperature-induced thermal stresses. Due to variations of temperatures
throughout the year, especially in hot regions, thermal stresses are induced
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