Titel_SS06

Xmax( )TXtXtXmaxT > 1 ( ) 2 ( ) ... n( )t? (7.27)

however, the assessment requires a detailed knowledge about the time variations of the
individual loads.

A general solution to Equation (7.27) is hardly achievable but solutions exist for special cases
of continuous processes and different types of non-continuous processes, see e.g. Melchers
(1987) and Thoft-Christensen and Baker (1982). However, approximate solutions to Equation
(7.27) may be established and in the following the most simple and most widely used of these
will be described.

Turkstra’s Load Combination Rule

By consideration of Figure 7.4 it is clear that it is highly unlikely (especially when the number
of loads is large) that all n loads will attain their maximum at the same time. Therefore it is
too conservative to replace the right hand side in Equation (7.27) with the term

maxTT>X 12 ( )tXt? max> ()? ... max (^) T>Xn( )t?. It is of course still unlikely (but less) that n 1
loads will attain their maximum at the same time but if the argumentation still hold in the
sense that the probability of simultaneous occurrence of a maximum of two of the loads is
negligible then Equation (7.27) may be solved by evaluating the maximum load for the
individual loads for the given reference period and combining them in accordance with the
scheme shown in Equation (7.28):

?
?

>?

1123

21 2 3

123

max ( ) ( ) ( ) ... ( )

() max () () ... ()

() () () ... max ()

T n

T n

nnT

Z Xt X t X t X t

Z Xt X t Xt X t

Z Xt X t Xt X t

44

44

444









4

4

(7.28)

and approximating the maximum combined load Xmax()T by:

Xmax() maxT (^7) i >Zi? (7.29)
This approximation is called Turkstra’s rule and is commonly used as a basis for codified
load combination rules.
The Ferry Borges – Castanheta Load Combination Rule
A more refined approximation to the load combination problem is based on the load model
due to Ferry Borges and Castanheta. This load model builds on a highly simplified
representation of the real load processes but facilitates a solution of the load combination
problem as defined by Equation (7.27) by use of modern reliability methods such as FORM
described in Lecture 6.
It is assumed that new realisations of each of the individual loads Xi take place at equidistant
intervals in time (^3) i and are constant in between. This is illustrated in Figure 7.5 where the
reference period T has been divided into intervals of equal length ni (^3) iTn/ i. is called ni