This is easily realised by considering the loading variables acting on a structural system, see
Figure 9.13.
P PQ12Batch 1 Batch 2M 1 = f 1 (P,Q)
N 1 = h 1 (P,Q)M 2 = f 2 (P,Q)
N 2 = h 2 (P,Q)Figure 9.13: Illustration of a structural system with two cross sections subjected to moment and normal
force.
The loading variables will normally all be represented in all the failure modes of the structural
system. The failure modes e.g. moment failure at location 1 and 2 are in for this reason said to
be functionally dependent.
Considering the resistance side of the modelling of structural systems the basic random
variables used to describe the resistances for the individual failure modes may be different but
are in most cases subject to some correlation. As an example consider again the frame
structure illustrated in Figure 9.5. The two different structural elements may have been
produced of steel from the same melt but were coming from two different material batches.
Therefore the resistance variables used to model the moment capacities at location 1 and 2 in
the steel frame are not the same but they may be correlated typically with a correlation
coefficient in the order of 0.6 – 0.7. The two failure modes considered are for this reason said
to be stochastically dependent.
9.4 Risk Based Assessment of Structural Robustness
Design codes have traditionally been developed with the main focus on the structural
reliability for individual failure modes or components of structures. System effects and
reliability of system failure modes such as full collapse are usually treated only by specifying
that structures should be design treated such that they are sufficiently robust. In general very
little guidance is provided by design codes on how to assess robustness and also in regard to
criteria for sufficient robustness.
The awareness of the significance of the robustness of structures was intensified some 40
years ago following the partial collapse of the Ronan Point. As a consequence a significant
amount of research has been invested into the various aspects of robustness and has resulted in
a number of useful recommendations on how to achieve robust structures. During the last 10