Dynamic/earthquake analysis - Computational Analysis and Design of Bridge Structures - page 526

Pressure,
P ( t )

Peak
pressure

Idealized impulse

Positive phase

Negative phase

P

Ambient
pressure

t d

Time of
arrival

Positive phase
duration

Negative phase
duration

Time, t

Figure 17.10 Pressure time history for free field blast. (Data from TM 5-1300, Structures to
Resist the Effects of Accidental Explosions , Department of Army, Washington,
DC, 1990.)

of the negative phase is much lower than that of the positive phase, and
usually the negative phase is neglected in the design. Only for light struc-
tures does the negative phase have a significant effect (Winget et al. 2005).
Although blast load is a dynamic load, equivalent static loads due to explosion
are usually used in assessing the structural performance because they impact
the structure for a very short duration. If dynamic effect is considered, the tran-
sient overpressure loads used on the right-hand side of Equation 17.1 can be
estimated where the decay of the reflected overpressure is assumed to obey the
modified Friedlander exponential decay equation, which can be written as

− α t t p /

p t ( ) = p [ 1 − t t / ] e (17.15)

m p

where:
p is pressure
p m is peak pressure
t p is positive phase duration
α is the waveform parameter

Since the structure behavior after sudden impact is localized, care must be
exercised when performing dynamic analysis; in particular, all high modes
of vibration should be included when using modal superposition or Ritz vec-
tor analysis methods. Direct step-by-step integration methods are preferable,
since such algorithms account for all possible vibration modes associated
with the given finite element mesh and analysis time step. Also considered in
dynamic analysis are nonlinear dynamic loads and thus nonlinear behavior.