a Com1: Load combination 1 (fixed load + live load + impact load).

b Com2: Load combination 2 (fixed load + live load + impact load + temperature load).

combination I and II in seven analysis cases. The limit state function in this study is:

to the bridge. The Pf of the limit state is calculated by the Rackwitz–Fiessler method [9]. The limit state function is:

where g() is a limit state function; MG is an internal resistant moment of the section; NG is a bias factor; ai is the coefficients of response function (i.e. regression equation of the random input variables as center and axis points, fitted from the response of a system).

Consequently, the resultant fitted response functions are obtained for the two load cases at two observation points, P1 and P2, as follows:

g() = MG NG − (57 347.6 + 0.029x1 − 0.141x2

where g() is the limit state function; SGn is shear strength of the section; NGSr is bias factor, and ai is the coefficients of response function.

The resultant fitted response functions for the two load cases at two observation points, P3 and P4, are shown in the following:

g() = SGn · NGSr − (3897.3 + 0.00022x1 − 0.00071x2

− 3.79 ∗ 10−7 x3 + 7.97 ∗ 10−12 x 2 + 1.78 ∗ 10−7 x 2

1 2

+ 3.91 ∗ 10−14 x 2

− 0.0001x3 − 4.649 ∗ 10−9 x 2

+ 2.26 ∗ 10−5 x 2 + 5.20 ∗ 10−12 x 2) (11)

3 ) (16)

g() = SGn · NGSr − (3920.1 + 0.000022x1 − 0.00039x2

2 3 − 8.83 ∗ 10−8 x3 + 9.28 ∗ 10−12 x 2 + 1.48 ∗ 10−7 x 2

g() = MG NG − (59 326.9 + 0.0305x1 − 0.107x2

1 2

+ 3.22 ∗ 10−14 x 2

− 0.000077x3 − 4.820 ∗ 10−9 x 2

+ 1.96 ∗ 10−5 x 2 + 4.66 ∗ 10−12 x 2) (12)

3 ) (17)

g() = SGn · NGSr − (3739.4 + 0.00021x1 − 0.00030x2

2 3 −7

−12   2

−8   2

− 4.54 ∗ 10

1x3 + 8.56 ∗ 10

x1 + 3.00 ∗ 10 x2

g() = MG NG − (34 348.9 + 0.00096x1 + 7.390x2

− 0.0011x3 + 1.08 ∗ 10−10 x 2 − 6.36 ∗ 10−4 x 2

+ 4.15 ∗ 10−14 x 2) (18)

1 2 g() = SGn · NGSr − (3795.0 + 0.00021x1 − 0.00027x2

− 2.02 ∗ 10−11 x 2) (13)

−8 −11   2

−8   2

− 8.83 ∗ 10

x3 + 1.02 ∗ 10

x1 + 2.93 ∗ 10 x2

g() = MG NG − (41 698.2 − 0.0011x1 + 8.180x2

+ 0.0011x3 + 1.18 ∗ 10−10 x 2 − 7.05 ∗ 10−4 x 2

+ 3.22 ∗ 10−14 x 2). (19)

1