Search

Despite a lot of effort has gone into research on human-induced vibrations of footbridges in the last decade, there is still a lack of reliable models and adequate design guideline pertinent to dynamic loading due to multiple pedestrians. There are three key issues that a new generation of models should urgently address: (i) interaction between pedestrians and the structure they occupy and dynamically excite; (ii) pedestrian intelligent behaviour; (iii) inter-subject and intra-subject variability of pedestrian walking loads. This paper presents a model of pedestrian-structure dynamic interaction in the vertical direction which addresses the first two issues. The model comprises three sub-models: (1) a model of a footbridge featuring a SDOF system having the dynamic properties of an empty structure, (2) a microscopic model of multiple pedestrian traffic that simulates position and velocity of each individual pedestrian in space and time, and (3) a model of individual pedestrian actuator featuring a periodic force model coupled with a spring-mass-damper oscillator which move together along the structure. The proposed model is applied to a lively footbridge with known modal properties and results are compared to the measured vibration response due to a light pedestrian traffic.

Because of inherent variability in all human cyclical movements, such as walking, running and jumping, data collected across a single cycle might be atypical and potentially unable to represent an individual's generalized performance. The study described here was designed to determine the number of successive cycles due to continuous, repetitive countermovement jumping which a test subject should perform in a single experimental session to achieve stability of the mean of the corresponding continuously measured ground reaction force (GRF) variables. Seven vertical GRF variables (period of jumping cycle, duration of contact phase, peak force amplitude and its timing, average rate of force development, average rate of force relaxation and impulse) were extracted on the cycle-by-cycle basis from vertical jumping force time histories generated by twelve participants who were jumping in response to regular electronic metronome beats in the range 2-2.8 Hz. Stability of the selected GRF variables across successive jumping cycles was examined for three jumping rates (2, 2.4 and 2.8 Hz) using two statistical methods: intra-class correlation (ICC) analysis and segmental averaging technique (SAT). Results of the ICC analysis indicated that an average of four successive cycles (mean 4.5 ± 2.7 for 2 Hz; 3.9 ± 2.6 for 2.4 Hz; 3.3 ± 2.7 for 2.8 Hz) were necessary to achieve maximum ICC values. Except for jumping period, maximum ICC values took values from 0.592 to 0.991 and all were significantly (p < 0.05) different from zero. Results of the SAT revealed that an average of ten successive cycles (mean 10.5 ± 3.5 for 2 Hz; 9.2 ± 3.8 for 2.4 Hz; 9.0 ± 3.9 for 2.8 Hz) were necessary to achieve stability of the selected parameters using criteria previously reported in the literature. Using 10 reference trials, the SAT required standard deviation criterion values of 0.49, 0.41 and 0.55 for 2 Hz, 2.4 Hz and 2.8 Hz jumping rates, respectively, in order to approximate the ICC results. The results of the study suggest that the ICC might be a less conservative but more objective method to evaluate stability of the data. Based on these considerations, it can be recommended that a force time history due to continuous, repetitive countermovement jumping should include minimum of four (the average from the ICC analysis) and possibly as many as nine successive jumping cycles (the upper limit of the ICC analysis) to establish stable mean values of the selected GRF data. This information is important for both experimental measurements and analytical studies of GRF signals due to continuous, repetitive countermovement jumping