Additionally, traffic volume and therefore the number of loading
events on bridges also tend to increase accelerating the rate at
which damage accumulates.
Fig. 1 illustrates the described changes of loading S and resistance
R over time. Discrete values for S and R are usually not available
and therefore they are assumed to be distributed according to
some probability functions. The area under the intersecting parts
of these two probability functions is a measurement for the probability
of failure. The initial position of these curves at time t = 0
illustrates the situation immediately after completion of a structure,
and the dotted lines in Fig. 1 show the situation at some later
point in time during the design life. In the present paper, the term
damage is used in the sense of a reduction in structural resistance.
Accumulated damage as a result of many loading events throughout
the life time of a structure causes a steady decrease of resistance.
It can be assumed, that the probability of failure remains below
the defined critical level throughout the life time of a structure
as long as these damage loading events remain within the regulations
of the applied design code indicated by the dotted line labeled
‘Design loading’ in Fig. 2.