Markov Renewal Model for Maximum Bridge Loading

Abstract

The prediction of maximum vehicle loadings on a bridge is studied. The stationary distribution of the static response of highway bridges under random truck loading is obtained using a Markov Renewal Model. This model is a generalization of Markov chains and renewal processes and can be used to model the arrival of trucks on a multilane bridge. The model also accounts for random truck characteristics such as axle weights, axle spacings, speed, and the headway distribution between trucks. The stationary distribution of the response is obtained assuming that the bridge (represented by its influence line) acts as a filter to the truck arrival process. The maximum lifetime response is obtained from the stationary distribution using an approximation to Rice's up‐crossing rate formula. The results are then compared to a simulation program and acceptable agreement is reported.