The inverted pendulum pedestrian model (IPM) for walking on laterally-oscillating structures, originally proposed by Macdonald, has been recently calibrated based on data from pedestrians walking on a laterally-oscillating instrumented treadmill. It was then generalised to be suitable for the application in a predictive manner, i.e. in simulations of lateral structural response for any population of pedestrians. The generalised IPM captures the fundamental pedestrian-structure interaction mechanism and pedestrian-generated lateral forces onto a structure, including the self-excited forces which are critical from the point of view of structural stability. However, since the closed-form solutions of the generalised IPM are currently unavailable, its application requires numerical integration. To address this shortcoming, closed form solutions for the long-term average lateral self-excited forces are derived in this study based on the framework introduced by McRobie. A parametric study is conducted revealing complex interdependencies between pedestrian and bridge behaviour and their influence on the self-excited forces. The presented results are related to the measurements from full-scale bridges and laboratory investigations.
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