This point is evident when there is an error in the assumed failure mode and order. The error can be caused by a correlation among the members. For example, two identical components composed of the same material and same manufacturer can fail at the same time under the same environmental condition, regardless of the distribution of structural stress load. Therefore, assuming the failure of important components to be statistically independent or fully correlated, the upper and lower bound of the probability of combined failure modes can be predicted by combining such component’s failures. Due to the assumption of correlation among failure modes, the suggested method
Fig. 4. Side view and observation points for the target bridge.
provides upper and lower bounds for the probabilities of failures.
The time–cost saving effect increases significantly with the increase in correlated components (Fig. 2). For example, when 20 failure cases of components are considered, the permutation method yields 2.433 × 1018 possible failure modes, the same number of possible modes for the structural analyses. That is
2.32 × 1012 times larger than the number of possible modes to be considered by the proposed combination method.
3. Reliability evaluation based on response surface method
3.1. Target bridge
An arch bridge in Korea is considered for the analysis at the preliminary design stage before the construction. The bridge is designed to resist ultimate limit states of flexure, shear, and buckling conditions. The finite element model for the bridge system is shown in Fig. 3, which shows 1492 nodes and 1570 frame elements. The bridge has 2 lanes and is 14.3 m in width and 360 m in span length.
Fig. 4 shows the critical components, which are determined based on the results of finite element analysis for the evaluation of component reliability. The observation points in Fig. 4 are for each risk event due to the failure of critical components.
1564 A.S. Nowak, T. Cho / Journal of Constructional Steel Research 63 (2007) 1561–1569
Table 2
Probabilistic properties of random variables
Random variables Bias
fac- tora
C.O.V.bReference
Fig. 5. The section considered to check the stress under tensile axial force with flexural moment.
Arch ribs
Axial strength f PU 1.05 0.10 Assumed
External axial force f E 1.05 0.10 Nowak [8]
Table 1
Girders Elasticity of steel ES 1.00 0.06 Tabsh and Nowak [7]
External force acting on the section of tie-girder (kN)
Flexural resistant moment
MR 1.12 0.135 Tabsh and Nowak [7]
Resistant shear force SR 1.08 0.12 Nowak [8]
External flexural moment
ME 1.05 0.10 Nowak [8]
Maximum 540.310 152.830 161.440 622.410 13 163.770 钢筋混凝土倒T梁采用锚固CFRP片材的修复英文文献和中文翻译(4):http://www.youerw.com/fanyi/lunwen_78834.html