The probabilistic distribution and statistical parameters obtained from the literature survey and assumptions are shown in Table 2.

4.2. Limit state function for the flexure failure of main girders

The flexure limit state function is established by the girder’s ultimate resistance and external negative maximum moment as it is fitted by the response surface method. The random variables’ response function uses the Bucher–Bourgund method for the average of random variables and three axial points. The selected random variables are section area, inertia, and resistant moments of the girders (Table 3). Since the Bucher–Bourgund method is used, the three axial points    had

the distance ±σ (standard deviation) between the center and axis points.

The statistical values of the selected random variables, which compose the response surface function, are provided in Table 4. The Pf of the limit state is calculated by the Rackwitz–Fiessler method [9], using probability distribution statistical parameters (Table  3).  The  reliability  index  is  calculated  for  the   load

A.S. Nowak, T. Cho / Journal of Constructional Steel Research 63 (2007) 1561–1569 1565

Table 4

Statistical values for the considered random variables

Cases Random variables P1 P2

x 1 x 2 x 3 Com1a

Com2b

Com1a

Com2b

CASE1 2.47E+06 3.54E+03 1.45E+07 101 080.48 104 970.76 62 184.37 71 754.91

CASE2 2.77E+06 3.54E+03 1.45E+07 102 600.37 106 540.27 62 066.54 71 627.52

CASE3 2.17E+06 3.54E+03 1.45E+07 98 723.84 102 533.47 62 321.67 71 903.62

CASE4 2.47E+06 3.97E+03 1.45E+07 101 093.19 104 988 63 309.96 72 996.61

CASE5 2.47E+06 3.12E+03 1.45E+07 101 076.15 104 960.92 60 857.94 70 290.55

CASE6 2.47E+06 3.54E+03 1.60E+07 101 166.68 105 069.1 62 872.11 72 464.1

CASE7 2.47E+06 3.54E+03 1.31E+07