On random spatial distribution of active crowds on grandstands and their effects on dynamic response

Abstract Active spectators on grandstands can induce wide palette of loads ranging from hand-clapping or swaying to bobbing or synchronized jumping. Each of these loads may differ in its intensity, frequency range, and level of synchronization. All these aspects render the process of predicting the behaviour and performance of grandstands difficult, requiring proper modelling techniques. Although grandstands themselves can be successfully modelled by finite element method, the situation with human-induced loading is less transparent, and mathematical description of load have evolved over the years from equivalent static load through deterministic approximations in time and frequency domain to Monte Carlo (MC) generators. In this contribution, the most intensive kind of human activity exercised on grandstands—synchronized jumping—is focused on. In particular, the response of grandstands loaded by jumping active crowds that are randomly distributed in space is investigated. For simplicity, no passive spectators are considered. Two modelling approaches are used. First, direct MC simulation provides a reference solution. Second, a semi-analytical formulation employing theory of random processes provides response estimates and simplifying formulas. Finally, both approaches are demonstrated and compared on a simple example.