Page 249 - Forensic Structural Engineering Handbook

LOADS AND HAZARDS: THEIR NATURE, MAGNITUDE, AND CONSEQUENCES 7.33

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effective pressure that is as much as 8 times the incident pressure. In fact, pressures up to
20 times the incident pressure have been measured when incident pressures are orders of
magnitude larger than atmospheric pressure. 28
At oblique angles of incidences, the magnification of pressure through reflection dimin-
ishes with angle. Reductions generally are relatively small until the angle between the inci-
28
dent shock front and the normal to the surface are approximately 40°. At larger angles,
the magnification diminishes rapidly.
As the pressure front passes the near surface of the building, the building begins to
become engulfed by compressive forces that act on all surfaces. First the near face experi-
ences a step increase in pressure that is the sum of the incident and reflected fronts. Then
the shock front passes the near face and momentarily engulfs the roof and sides of the build-
ing. Pressure fronts passing the sidewalls and roof normally are not amplified by reflection,
but these surfaces do experience first pressure variations due to compression of the air and
then potentially reversing pressures due to the explosion “winds” and vortices created by
building edges. As the shock front progresses along the depth of the building, the pressure
on the front face drops because the reflected front leaves this surface and travels back
toward the detonation point. In a fraction of a second, the pressurized gas has reached the
far face of the building, and that wall experiences compressive forces as diffraction of pres-
sure fronts around corners contributes to the development of significant pressures on all
surfaces. The entire loading cycle is completed in tenths of a second or less.
At this point, the building and its components have been set in motion by the pressure
impulses that they experienced, and their ability to survive depends on their ability to
absorb and dissipate the acquired kinetic energy. The analysis of the response of the struc-
ture rarely can be treated as a static or quasistatic phenomenon. Consideration must be
given to the dynamic response of the structure to the very short-duration loading cycle, and
to the inelastic response necessary for building components to absorb the imparted energy.
For explosives that are detonated close to buildings, there can be very significant vari-
ations of pressure on near surfaces [e.g., variations in effective pressures on the near wall
2
of the Murrah Building in Oklahoma City exceeded 10,000 lb/in (70 MPa) at ground level
2
near to the detonation point, and diminished to less than approximately 10 lb/in (0.3 MPa)
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at the more remote portions at the top of the near face of the building]. This occurs pri-
marily because the radial distances to different portions of the near surface are substantially
different. Also, as the shock front progresses up and away on a building face, the incident
and reflected fronts can combine and magnify effective pressures much as they do in air
explosions.
In urban environments with many closely spaced buildings, blast effects can be further
magnified. First, many complex reflections can occur when an explosive is detonated
between buildings that line often narrow city streets. Then, when large explosives are det-
onated between tall buildings on very narrow streets, the expansion of gases is not entirely
free. Through reflection and diffraction, the significant effects of major explosions can be
felt around corners and on streets adjacent to explosion sites.
Buildings with overhangs, recesses, and reentrant corners can experience dispropor-
tionate damage. These features, which allow the shock front and expanding gases to pass
into a partially confined space, can substantially magnify the pressures exerted on a build-
ing’s facade through reflection of the blast pressures and confinement of expanding gases.
Structural elements also receive shock loads that can destroy elements before their
structural strength can be mobilized. When the shock from a blast strikes the near surface
of a hard object, the shock sets in motion a compressive wave that travels through the mate-
rial. When this wave reaches the far surface of the object, some of its energy is transmitted
out of the object (to the air) and some energy is reflected from the back surface through the
object again. The reflected wave in the object now is a tension wave. Concrete and other
materials that are strong in compression and weak in tension might be able to sustain the