Around the world, an increasing amount of bridge infrastructure is ageing. The resources involved in the reassessment of existing assets often exceed available resources and many bridges lack a minimum structural assessment. Therefore, there is a need for comprehensive and quantitative approaches to assess all the assets in the bridge network to reduce the risk of collapsing, damage to infrastructure, and economic losses. This paper proposes a methodology to quantify the structural criticality of bridges at a network level. To accomplish this, long-run site-specific simulations are conducted using Bayesian Networks and bivariate copulas, utilizing recorded traffic data obtained from permanent counting stations. To enhance the dataset, information from Weigh-in-Motion systems from different regions was integrated through a matching process. Subsequently, the structural response resulting from the simulated traffic is assessed, and the extreme values of the traffic load effects are obtained for selected return periods. Site-specific bridge criticality as a performance indicator for traffic load effects is derived by comparing the extreme load effects with the design load effects. The outcomes are mapped to facilitate visualization employing an open-source geographic information system application. To illustrate the application of the methodology, a total of 576 bridges within a national highway network are investigated, and a comparison with a popular simplified method is shown. The methodology herein presented can be used to assist in assessing the condition of a bridge network and prioritizing maintenance and repair activities by identifying potential bridges subjected to major load stress. • Methodology for mapping extreme load effects due to heavy vehicles in bridge networks • Evaluation of bridge criticality as a performance indicator for traffic load effects • Simple yet robust method using Bayesian Networks and copulas for traffic simulation • Application of the methodology to Mexico's national bridge network as case study [ABSTRACT FROM AUTHOR]