A History of Research and a Review of Recent Developments

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Structural loading from distant explosions
Figure 4.1 Blast wave meeting 180° semi-circular arch (from Newmark et al., ref.
4.2).
maximum average pressure on the front of the cylinder is 2p, and that this
decays linearly until a time 2D/ū. The average side loading is given as
in ref. [4.5], and the maximum back surface loading as
p(20D/ū)+C dq(20D/ū).
When a semi-cylindrical, or arched structure is loaded by a shock wave perpendicular
to its longitudinal axis, vortex formations can occur immediately after reflection,
so that a temporary sharp drop can occur before the stagnation pressure is reached.
Subsequently the total pressure, p+C dq, decays in the usual way. The relationship
between p 1, p 2, C d and the angle a for a semi-circular arch is shown in Figure 4.1,
where p 1 and p 2 are related to p r, the ideal reflected pressure for a free surface.
Since the structural loads are normal to the surface, the total horizontal load on
the structure is formed by summing all horizontal components, and Figure 4.1
gives the approximate equivalent net horizontal force.
Many arched structures are not fully semi-cylindrical, and for 120° arches
similar relationships to those in Figure 4.1 have been presented (see, for example,
ref. [4.2]). It can be seen from these relationships that C d varies from positive
to negative as the angle increases, and is also influenced by the peak incident