where N is the set of real positive numbers.
The combined load effect following the combination rule due to Ferry Borges – Castanheta
may now be established by evaluation of
Xmax() maxT (^7) i >Zi? (7.33)
where Zii, 1, 2,.., 2r^1 correspond to different cases of load combinations. For the
load cases to be considered are given in
r 3
Table 7.4.
Load combination Repetition numbers
Load 1 Load 2 Load 3
(^1) n 1 nn 21 / nn 31 /
2 1 n 2 nn 32 /
3 1 1 n 3
(^4) n 1 1 nn 31 /
Table 7.4: Load combinations and repetition number to be considered for the Ferry Borges –
Castanheta load combination rule.
7.3 Probabilistic Modelling of Resistances
In the following resistance variables are understood as any random variable affecting the
ability of a considered technical component or system to withstand the loading acting from the
outside. The resistance is thus to be understood as a characteristic of the interior of the
considered component or system.
As for the loading the following treatment of resistance variables will be related to structural
reliability analysis but as before the philosophy and concepts will be applicable to other fields
of risk and reliability engineering.
Typical resistance variables in structural reliability analysis are:
Geometrical uncertainties
Material characteristics
Model uncertainties
The important issue concerning the probabilistic modelling of resistances is to represent their
random variations both in time and space.
Having identified the characteristics of the considered resistance variable the probabilistic
modelling may proceed by:
defining the random variables used to represent the uncertainties in the resistances
selecting a suitable distribution type to represent the random variable
assigning the distribution parameters of the selected distribution.