A comprehensive evaluation of a structure’s performance based on quasi-static measurements requires consideration of the response due to all applied loads. For the majority of short- and medium-span bridges, temperature and vehicular loads are the main drivers of structural deformations. This paper therefore evaluates the following two hypotheses: (i) knowledge of loads and their positions, and temperature distributions can be used to accurately predict structural response, and (ii) the difference between predicted and measured response at various sensor locations can form the basis of anomaly detection techniques. It introduces a measurement interpretation approach that merges the regression-based thermal response prediction methodology that was proposed previously by the authors with a novel methodology for predicting traffic-induced response. The approach first removes both environmentally (temperature) and operationally (traffic) induced trends from measurement time series of structural response. The resulting time series is then analysed using anomaly detection techniques. Experimental data collected from a laboratory truss is used for the evaluation of this approach. Results show that (i) traffic-induced response is recognized once thermal effects are removed, and (ii) information of the location and weight of a vehicle can be used to generate regression models that predict traffic-induced response. As a whole, the approach is shown to be capable of detecting damage by analysing measurements that include both vehicular and thermal response.