PSI - Issue 78

Amirmahmoud Behzadi et al. / Procedia Structural Integrity 78 (2026) 513–520

519

5. Simplified Design Equations To facilitate practical application, linear regression models were fitted to the results from Scenario 2 (most conservative). The braking force F bf was expressed as a function of bridge span L , return period T R , and nominal life V N , Eq.2: = ( ) + ( ) , , N b R R N f F T V L T V    (2) where α and β are functions of TR and VN, calibrated through regression as depicted in Fig. 7 and 8. These simplified expressions provide engineers with easy-to-use formulas for estimating braking forces tailored to specific design conditions.

Fig. 7. α coefficient .

6. Conclusions This study presents a novel Probabilistic Braking Force Model (PBFM) that uses real-world WIM traffic data and Monte Carlo simulations to estimate braking forces on bridges more accurately within a probabilistic design framework. Unlike traditional deterministic models with fixed assumptions and undefined return periods, the PBFM accounts for variability in vehicle weight, length, spacing, and deceleration to link braking force values directly to specified return periods. Results show that while existing codes like EC1-2 may be conservative for short spans, they can underestimate forces for longer spans, highlighting the need for probabilistic approaches. The model offers braking force estimates for various return periods (500 and 1000 years) and nominal lives (5, 30, and 50 years), supported by simplified regression-based equations, making it a practical and adaptable tool for both new bridge design and the assessment of existing structures.