Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 523

17.2.3.2 Nonlinear time-history analysis
Time-history analysis (THA) is a step-by-step analysis of the dynamical
response of a structure to a specified loading that may vary with time through
a process of numerical integration of the equations of motion. It involves the
development of a complete mathematical model of the bridge wherein an effort
is made to model nonlinear forms of behavior in a highly localized (rather than
global) manner. The mathematical model is formulated in such a way that the
stiffness and even connectivity of the elements can be directly modified based
on the deformation state of the structure. This permits the effects of element
yielding, buckling, and other nonlinear behavior on structural response to be
directly accounted for in the analysis. The model is then subjected to time
histories of earthquake ground acceleration that may be in either historical
records or design spectrum compatible records. In either case, an attempt is
made to capture the full time history of the nonlinear structural response.
The use of multiple records in the analyses allows observation of the dif-
ference in response resulting from differences in record characteristics. As a
minimum, suites of ground motions include at least three different records
(FEMA-450 2003).
Different from linear THA, the differential equations of motion for non-
linear THA (NL-THA) cannot be considered as smooth functions. It is due
to the nonlinear hysteresis of most bridge structural materials, friction forces
developed between contacting surfaces, and buckling of elements. Therefore,
only step-by-step methods are recommended for the solution of the nonlinear
time history of bridge structures. The step-by-step solution methods attempt
to satisfy dynamic equilibrium at discrete time steps and may require itera-
tion, especially when nonlinear behavior is developed in the structure and
the stiffness of the complete structural system must be recalculated due to
degradation of strength and redistribution of forces (Aviram et al. 2008).
Unlike linear time history, the nonlinear case can take a significant
amount of time to solve structural systems with just a few hundred DOFs.
Engineers must be careful in the interpretation of the results and check the
results using the applicable acceptance criteria. An example of a bridge case
analyzed by linear THA and NL-THA methods plotted on the same graph
is shown in Figure 17.9.
17.2.4 Blast loading analysis
Blast loads are considered as most extreme loads, and even a small amount
of blast can produce a serious damage to the structure. The blast wave
produced by explosion travels even faster than the speed of sound. When
it arrives at a location, it causes a sudden rise in the normal pressure. The
increase in atmospheric pressure over normal values is referred to as over-
pressure, and the simultaneous pressure created by the blast winds is called
dynamic pressure. Blast pressure can create loads on structure that are