Variable

Mean $(4)$

STD $(0)$

$10$ kN$/$m

$0\mathrm{.}4$ kN$/$m

$2\backslash$times$10^\{7\}$kN$/$m$^\{2\}8\backslash$times$10^\{-4\}$m$^\{4\}$

$0\mathrm{.}5\backslash$times$10^\{7\}$kN$/$m$^\{2\}1\mathrm{.}5\backslash$times$10^\{-4\}$m$^\{4\}$

W

A

D

C

L

L

L

$8.(20$ pts$)$ Consider the three$-$span continuous beam shown above. The limit state function

for this beam is

g$=\backslash$frac$\{$L$\}\{360\}-0\mathrm{.}0069\backslash$frac$\{$wL$^\{4\}\}\{$EI$\}$

Use the Monte Carlo method to calculate the probability of failure and the reliability index for the beam. Assume all random variables are normally distributed and uncorrelated and use L$=5$~m