## 0y2

2 540336 10-3

\J(-1.166536 x 10-3)2 x 0 .3 + (-2 .540336 x 10-3)2 x 1. 7

-6.38938 x 10-4 3 .373257 x 10-3 -2 .540336 x 10-3 x pL7

During the first iteration, no comment can be made about the convergence of the direction cosines. As shown in Table 12.2, the direction cosines converged during the third iteration with a tolerance level of 0.005. Then, Task 7 can be carried out as shown below. Task 7

y* = 0 .1491 x p03b = 0 .081665b y2* = 0 . 9890 x VT^b = 1.289498b The applicable limit state function, similar to Equation 12.29, can be shown to be

= 0 .01131131 - 9 .715649 x 10-4Y1 - 2. 7353082 x 10-3Y2

Thus

0 .01131131 - 9. 715649 x 10-4 x 0 .081665ß - 2 . 7353082 x 10-3 x 1.289498ß = 0

Final iteration

As shown in Table 12.2, the operating value for b is 3.136 and the direction cosines values are —0.1425 and —0.9848. Task 3

y* = 0.1425 x ^03 x 3.136 = 0.24476 y* = 0.9898 x x 3.136 = 4.0471

w* = 3.711(0.24476 + 4.0471) + 35.03 = 50.957 p* = 10.384(—0.24476 + 4.0471) + 105.221 = 144.704

Task 4. The applicable mean and standard deviation values for w and P are given in Table 12.2. Tasks 5 and 6. The applicable limit state function, similar to Equation 12.30, can be shown to be g() = 0.0113564 — 9.594176 x 10—4Y1 — 2.74745 x 10—3 Y2 (12.31)

M) = —9.594176 x 10—4 and ^ = —2.74745 x 10—3 0Y1 0Y2

\J(-9.594176 x 10-4)2 x 0.3 + (-2.74745 x 10-3)2 x 1.7 — 5.2549466 x 10-4

3.62057498 x 10-3

0 0