Seismic Analysis of Structures: Improvements Due to Probabilistic Concepts - Dynamic Behavior of Concrete and Seismic Engineering - page 290

Figure 8.6. Rate of the reliability function - comparison between the different
estimations for a narrow-band process

The function W varies from 0 to 1 when r varies from 0 to infinity. The crossing
occurs quite suddenly around such r-values as W(r) = ½, which is an increasing
function of N (Figure 8.6).

Thus, we can explain integral [8.30] owing to expression [8.32]. If N is not too
large (N t 100), we have:

1/ 2

ȝ N2 nN ¬ ª º

[8.33]

¼

It is also possible to explain the maximum standard deviation (related to the
process standard deviation):

1/ 2

)

@ 1/ 2 > ma ı N ʌ 6

2 n (

[8.34]