Serviceability assessment of footbridges via improved interval analysis

This paper studies the propagation of uncertainties on serviceability assessment of footbridges in unrestricted traffic condition based on a nondeterministic approach. Multipedestrian loading is modeled as a stationary Gaussian random process through the equivalent spectral model which yields analytical expressions of the spectral moments of the footbridge dynamic response. The uncertain pedestrian-induced loading parameters and structural dynamic properties are modeled as interval variables. An approximate analytical procedure, based on the improved interval analysis, is introduced as an efficient alternative to classical optimization in order to propagate interval uncertainties. The presented procedure allows us to derive closed-form expressions of the bounds of the spectral moments of the response, as well as of the expected value and cumulative distribution function of the maximum footbridge acceleration. Two strategies are proposed to assess footbridges' serviceability. The first one leads to the definition of a range of comfort classes. The second strategy enables us to estimate an interval of probability of reaching at least a suitable comfort level.