value

P1 and P2 indicate the observation points for the tie-girder’s flexural failure, P3 and P4 are the observation points for the girder’s shear failure, and P5 and P6 represent the axial failure points of the arch ribs, where the stiffening member to resist moment and shear is the girder at road level, which also acts as the tie. Thus, the tensile force has been checked for the possibility of failure by the finite element analysis. In the considered section of P1 and P2, the maximum tensile force (Table 1) makes ignorable stresses at the upper area of the section of girder as evaluated in three equations as:

ft  + fbty + fbtz  ≤  fta :

2.852 + 79.277 + 1.091 = 73.220 ≤ 210.0 (7)

External shear force SE 1.05 0.10 Nowak [8]

a Bias factor: Ratio of actual values to nominal values.

b C.O.V.: Coefficient of Variation (as standard deviation pided by mean value).

Table 3

Statistical values for the considered random variables

Random variable Name Mean value C.O.V. Distribution

I zz1a x 1 2.47E+06 0.12 Normal

Area x 2 3.54E+03 0.015 Normal

I zz2b x 3 1.45E+07 0.12 Normal

MG x 4 2.27E+10 0.10 Log normal

a I zz1: Inertia of the girder in horizontal axis.

b I zz2: Inertia of the girder in longitudinal axis, MG : External moments.

4. Component reliability by response surface method

In the following, the limit-state function for each component

is developed, and reliability analyses for each component and for the system are performed.

210.0 + 210.0 = 0.184 ≤ 1.0 (8)

4.1. Random variables and statistical parameters

− ft  + fbcy + fbcz  ≤ fcal   :

−2.852 + 36.570 + 4.890 = 38.608 ≤ 1261.151 (9)

where ft : tensile stress (=2.852 MPa); fbty : flexure tensile stress (=69.28 MPa); fbtz : flexure tensile stress (=1.091 MPa); fbtz : flexure compressive stress (=–36.570 MPa); ; fbtz : flexure compressive stress (=–4.890 MPa); fta : allowable tensile stress (=210 MPa); fbay : allowable flexural compressive stress (=210 MPa, local buckling ignored); fbao: the maximum allowable flexural compressive stress (=210 MPa, local buckling ignored); and fcal : allowable stress (depending on thickness = 1261.151 MPa) (see Fig. 5).

Shown in Fig.  5,  the  considered  section  has  inertia  as: Iz = 5.175E11 mm4, I y  =  3.763E11  mm4,  the distance from centroid to top as 2321.9 mm, from centroid to bottom

as 518.1 mm, and the distance from centroid to right end as

1045.5 mm, from centroid to left end as 1980.5 mm, The type of steel is SM520 (tensile strength = 520 MPa).

Due to the small amount of tensile stress by the “tie-effect” in the section, in this study the tensile external axial load effect has been ignored.