This thesis presents a novel methodology to determine the reliability of cantilever grandstands under dynamic crowd loading. No method currently exists to evaluate this, despite the occurrence of significant vibrations in such structures, for example in the Feyenoord Stadium in R
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This thesis presents a novel methodology to determine the reliability of cantilever grandstands under dynamic crowd loading. No method currently exists to evaluate this, despite the occurrence of significant vibrations in such structures, for example in the Feyenoord Stadium in Rotterdam. These vibrations can negatively affect both the safety and serviceability of such structures, so a method able to evaluate both is desirable. The methodology consists of four components: a model of a grandstand, a model of the dynamic crowd load, a failure criterion, and a reliability analysis. Of these, the first and third component are case-specific, as a wide range of different grandstands and different criteria could be considered. In this thesis, the methodology is applied on a case study based on the Feyenoord Stadium, with a model of the trusses beneath the main grandstand of this stadium, and a criterion based on the intensity of the vibrations of the upper cantilever of this grandstand, a serviceability issue. The second component represents the most novel aspect of the methodology: a model describing the dynamic crowd load, defined in the frequency domain, and generally applicable regardless of the structure being considered. The core of this model is a parameterisation of the amplitude spectrum of the load applied by a group of jumping spectators. The parameters describing the spectrum are considered as stochastic variables, with distributions fitted using samples from a state-of-the-art database of measured loads. As opposed to the first and third components, this load model should be generally applicable.The parameters of the load model, together with other stochastic variables in the grandstand model, form the input of a Limit State Function. The output of this function determines whether the structure loaded by the crowd meets a certain criterion, and forms the basis of a reliability analysis together with the distribution of the stochastic variables. The probability of \emph{not} meeting the criterion, the failure probability, is calculated through a number of reliability methods in the final component of the methodology. These methods should be generally applicable as well, though which methods fits the best could still depend on the case being considered. This methodology was successfully applied on the case study, and a failure probability was found with two different methods. One of these, Crude Monte Carlo, allowed for a more fluid view of the concept of `failure' when a serviceability criterion based on a subjective limit is considered. The other method, SDARS, returned a slightly larger failure probability, in a much shorter runtime than Monte Carlo. This method is therefore more fit for safety criteria with a small (expected) failure probability, for which Monte Carlo would require an unreasonably long runtime. In addition, the wider applicability of the methodology has been investigated. An important requirement for this is flexibility with regards to the applied reliability methods. Two other methods, Directional Sampling and SDARS, were also attempted but did not yield usable results. This is caused by the manner in which phase angles are defined in the frequency-domain model. Random values are drawn, which causes noise to appear in the limit state function: a constant input does not lead to a constant output. Being able to use different reliability methods is an important requirement for applying the methodology in a wider variety of cases. In order to apply these methods, the phase angles need to be defined in a manner which does not introduce noise. Another important requirement is the ability to consider different failure criteria. While the criterion applied in the case study could be evaluated in the frequency domain, many others will require the results to be transformed to the time domain. Applying this transformation to the frequency-domain results of the models currently does not yield usable results, which is likely also caused by the definition of the phase angles in the load. In conclusion, while the methodology is applicable on the case study, the definition of the phase angles requires attention before it can be applied on other cases.