Interval solution and robust validation of uncertain elastic beams

In the field of structural mechanics the notion of uncertainty is employed in several contexts such as modelling, analysis, experiments, and reliability. When dealing with problems involved with uncertainty the model of the system should include an appropriate representation of the uncertain quantities. Among different formulations capable of representing uncertainties, certainly interval analysis promises to be very effective since it is not required to handle distributions as where probability is concerned. In this work the attention will be focused on the so-called direct problem where the mechanical model and the amount of uncertainty in the parameters are a priori given and the goal is to evaluate how and to what extent the uncertainty propagates and influences the response of the system. In this context, the uncertainty may come from the scarce knowledge about the materials, geometry and boundary conditions that constitute the structural model. An example of this is the uncertainty in loading, which intensity, area and location contribute to shape the mathematical equations that describe the problem. The purpose of the paper is to go through the use of the interval formulation as alternative to the probability formulation in the study of systems embodying uncertain parameters. Sample problems concerning the statics of beams will be addressed and the interval solution will be discussed and compared to analytic or Monte Carlo probability solutions. The effectiveness of the presented approach is demonstrated by means of a real case example, where a set of precast concrete beams undertaking static tests is analysed.