A History of Research and a Review of Recent Developments

Load factor 225
expected number of fragments that could hit the structure without ricocheting
using a simple spray pattern (cylindrical or spherical). The third step is to
select a design fragment and find its lethality (based on penetration); using a
formula for concrete as an example, lethality=, where W f is fragment weight
(lbs) and V s the striking velocity (feet/sec). This formula is likely to be very
conservative. The next steps are to calculate the probability that no fragments
with a lethality greater than the design fragment will be generated by the
exploding bomb, and to calculate the expected number of lethal fragments in
the total fragment population. The final stages are to select a size of design
fragment so that the desired level of reliability is achieved and there will be no
lethal hits. This fragment is then used in the design of the protective structure.
The method relies on a large amount of reliable experimental data that has
been analysed on a probability basis to provide fragment weight and velocity
distributions, and whether this could be assembled for a full range of weapons
and circumstances is debatable.
All this research has to do with load factors, but before the overall safety
level of a structure can be assessed these factors must be combined with structural
resistance factors. Twisdale and his colleagues looked at this problem for
loads due to projectiles and fragments, and their preliminary findings were
reported in reference [9.28]. They took as an example the design of a reinforced
concrete wall to resist 30 mm cannon fire with a 95% reliability, and used
load factors based on existing databases for small projectiles impacting massive
concrete targets. From these databases 710 records were used, of which 534
gave depth of penetration and 703 gave information on spall and perforation.
A typical striking velocity coefficient of variation was 0.2, and for a reliability
of 95% the specified striking velocity needed to be multiplied by a load factor
(for concrete perforation) of 1.12. The factored striking velocity was then
used to calculate the minimum thickness of wall to prevent perforation. For a
reliability of 95% the calculated wall thickness was multiplied by a resistance
factor of 1.54, so that the overall safety factor was 1.12×1.54=1.8. Thus the
safety margin for 95% reliability in design against projectile perforation looks
to be less than that for a structure under incident air blast, where just the load
factor might be of the order of 2.0. These figures are influenced of course by
the coefficients of variation of the experimental results, so too much should
not be read into them. They should be taken as an illustration of recent thinking
in the use of reliability-based analysis in the design of structures under the
threat of blast or penetrating weapons.
It is interesting to compare these factors with resistance factors proposed
by the author when discussing the design of underground protective structures
subjected to surface air-blast loading, given in reference [9.29]. Using engineering
judgement a load factor of 1.5 was proposed for dynamic pressures due to
explosions on the surface, and a resistance factor of 1.6 for strength variations
due to uneven soil compaction or the presence of ground water. For structures
in which close attention was paid to emplacement it was considered that the