Uncertainties in a beam model belonging to a residential tower

The starting point of this study are some student projects developed within the 2012 Mathematical Models inArchitecture and NumericalAnalysis Course, atArchitecture of Building School, Politecnico di Milano. It deals with different models of a beam for a residential tall building floor.Assuming that every existing structure can be analyzed by a more or less extended model (completeness) with different accuracy (concreteness), the provided modeling points out some approximate solutions. The study is developed starting from the most simple solution of a beam model up to considering the complete frame of the building. Progressively improving the most simple model, the relevance of common modeling hypotheses within structural design is shown. Comparing the above-mentioned models, different solutions can be achieved. Some unusual but interesting questions are pointed out. The apparent statement that "the more complete and concrete is a numerical model, the closer it is to the truth" may be misleading: The accuracy of a model depends on the data input availability. Since uncertainty often affects experimental data and mechanical theories are based on assumptions, the more data provided by the input model, the more uncertain is the model. Thus, the most complex model doesn't always provide the optimal solution. Apparent correspondence "the more complete and concrete is a numerical model, the closer it is to truth" may be misleading: The accuracy of a model depends on the data input availability. Since uncertainty often affects experimental data and mechanical theories are based on assumptions, the more data input model provides, the more uncertain the model is. The most complex model isn't always the optimal solution.