Titel_SS06

Now the first step is to transform the Normal distributed random variables R, and into
standardized Normal distributed random variables, i.e.:

A S

R

R

R

R

U









A

A

A

A

U









S

S

S

U S 



 

The limit state function may now be written in the space of the standardized Normal
distributed random variables as:

R

()()()(

(35 350)(1 10) (300 1500)

350u 350 300 35 2000

RR R AA A SS S

RA S

ASRA

gu u u u

uu u

uuuu

    )

 

 

The reliability index and the design point may be determined in accordance with Equations
(6.18) and (6.19) as:

2000

(^350) RAS R 350 300 35



5555A

 

 5

(^1) (350 35 )
55RAk
(^1) (350 35 )
55ARk
300
(^5) S k
with





350 35^22 350 35 300

k 5AR5

(^2)
which by calculation gives the iteration history shown in Table 6.1.
Iteration Start 1 2 3 4 5
 3.0000 3.6719 3.7399 3.7444 3.7448 3.7448
R -0.5800 -0.5701 -0.5612 -0.5611 -0.5610 -0.5610
A -0.5800 -0.5701 -0.5612 -0.5611 -0.5610 -0.5610
S 0.5800 0.5916 0.6084 0.6086 0.6087 0.6087
Table 6.1: Iteration history for the non-linear limit state example.
From Table 6.1 it is seen that the basic random variable Smodelling the load on the steel rod
is slightly dominating with an 5 -value equal to 0.6087. Furthermore it is seen that both the