PSI - Issue 84

Alessandro Lipari et al. / Procedia Structural Integrity 84 (2026) 615–622

621

10 12 14

Empirical

Gumbel

GEV

13392

11475

T = 1000 years T = 500 years T = 100 years T = 200 years T = 50 years

10542

0 2 4 6 8

11561

SEV

4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000

-4 -2

Bending moment (kNm)

Fig. 2. Gumbel probability paper plot of weekly bending moment maxima.

Table 2. Bending moments (values in kNm). Loading (partial safety factor)

Unfactored

Factored

LM1 ( γ Q = 1.5) LM1 ( γ Q = 1.2)

23367

15578

18694 (0.800) 17213 (0.737) 13770 (0.589) 12650 (0.541) 16397 (0.702) 13835 (0.592) 12435 (0.532) 10493 (0.449)

GEV 1000 years ( γ Q = 1.5) GEV 1000 years ( γ Q = 1.2) GEV 50 years ( γ Q = 1.2) CdS 44 t (Level 1, γ CdS,1 = 1.6) CdS 44 t (Level 2, γ CdS,1 = 1.35) CdS 26 t (Level 1, γ CdS,2 = 1.6) CdS 26 t (Level 2, γ CdS,2 = 1.35)

11475 (0.737)

10542 (0.677)

10248 (0.658)

7772.3 (0.499)

Note: in parenthesis ratio to full LM1 value. Table 2 shows that the GEV-extrapolated load effects to T = 1000 years are much smaller than LM1 (-26.3%), while keeping the safety level required by the codes. Consequently, if the factored bending resistance were above 17213 kNm, the bridge could be deemed in adequate conditions. Let us now assume that the factored bending resistance is 15000 kNm. In the absence of any site-specific traffic data, the bridge would be rated in transitable conditions, either with a 26-t weight restriction and sample weight checks, or with a 44-t weight restriction and continuous weight checks. When using site-specific traffic data, the applied bending moment reduces, thereby keeping the bridge in operational conditions, that is, without any restriction. It should be noted that T may be reduced when assessing structures using site-specific traffic data, for instance by considering n = t ref = 30 years in Eq. 2 while keeping the same probability of exceedance of 5% stated in EC1-2. This would correspond to T = 585 years but, as can be seen from Fig. 2, the load effects will not decrease significantly. Further reductions may be considered, provided that the traffic is monitored and periodically analysed to ensure that traffic characteristics do not become more onerous. As such, it is generally advisable to maintain T = 1000 years. Finally, it is worth mentioning that most bridges have obviously more than one lane. A practical way to deal with multiple lanes is to use the LM1 for lanes other than Lane 1 (Fig. 1). Alternatively, statistical combinations of different distributions may be applied with methods based on the law of total probability (Caprani et al., 2008). 7. Conclusions Traffic loading on bridges is highly variable and notional load models in codes of practice, such as in Eurocode 1, are effectively conservative for most real-world traffic conditions. This paper outlines how to use site-specific traffic data, typically collected from weigh-in-motion stations, for the structural assessment of existing structures within the