Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 525

2. SDOF linear/nonlinear dynamic analysis. This method is considered
the current state-of-practice method that ignores higher-order failure,
allowing for the analysis of a large number of load cases, bridge types,
and structural configurations.

3. MDOF, uncoupled/coupled, nonlinear dynamic analysis. This method
includes the finite element method (FEM) analysis. A coupled analysis
accounts for coupled effects of structural response with fluid dynamics
behavior of an explosion load, considering time and spatial coupling
while uncoupled analysis does not.

The most common and simplified blast dynamic analysis method used in prac-
tice is an SDOF or MDOF, uncoupled, nonlinear dynamic analysis. The loads
acting on a structure are usually determined using a shock-wave propagation
program. Once the loads have been determined, the structural response can
be analyzed using a dynamic structural analysis, accounting for the full plastic
capacity of the members. In an uncoupled analysis, the blast load calculations
are separated from the structural response. A coupled analysis, which is more
refined, performs the blast load calculations and structural response simulta-
neously. This technique accounts for the motion and response of structural
members as the blast wave proceeds around (or through) them and will mostly
provide a more accurate prediction of the structural response. Several tech-
niques exist for performing a coupled analysis, all of which involve time-space
discretization. Uncoupled analyses will usually provide conservative yet reason-
able results with much less effort and are best suited for typical design cases. The
LS-DYNA (1998) with FEA-coupled analysis as mentioned in Section 17.2.1
can also be used here to simulate the blast load-bridge interaction.
The dynamic response of bridge structures under a blast load is quite
complex due to the highly nonlinear nature of shock wave lasting around
several milliseconds. It is hard to analyze accurate deformation or crack
conditions of bridges subjected to blast wave. Nonlinear static analysis can
be used to analyze the bridge structures with blast loading. Therefore, the
blast pressures must be converted to equivalent static loads. In 1990, the
U.S. Department of Defense published the TM 5-1300 Manual, Structures
to Resist the Effects of Accidental Explosions . The manual contains an
empirical formula to find the scaled distance ( Z ) of a blast wave.

R
W

Z

= (17.14)

1 3 /

In Equation 17.14, R is the standoff distance of an object from the blast cen-
troid, measured in feet, and W is the charge weight of TNT in pounds. The
TM 5-1300 Manual (1990) contains a chart using this empirical formula.
A typical pressure time-history curve in free field is shown in Figure 17.10.
The positive phase is usually idealized to an equivalent triangular blast load
having the same peak pressure and an idealized duration ( t d ). The amplitude