The paper reports the results of a blind benchmark developed as a part of the preliminary activity of the research project RiSEM (Italian acronym for Seismic Risk on Monumental Buildings). The benchmark was aimed at comparing the results obtained with different analytical models and/or numerical analysis techniques (variational approach, finite elements, macroelements, equivalent frame, etc.) for the assessment of the nonlinear structural behavior of two cantilever masonry elements with different slenderness. The analyzed elements were characterized by a deliberately simple geometry, and the comparison between the numerical results had a twofold purpose. On the one hand, it aimed at estimating the effects of the epistemic uncertainties that are related to the different models and numerical techniques. On the other hand, it aimed at reaching a proper evaluation of the influence of parameters describing the postelastic behavior of the structural typology analyzed within the research project (specifically, the masonry towers). Both these objectives were necessary to further proceed with the development of simplified numerical models needed for the subsequent risk analysis. For both slendernesses, the results have highlighted a significant dispersion of both the displacement capacity and postpeak softening branch of the capacity curves. In addition, after some elaborations it has been observed that the dispersion of the results is proportional to both the shear-force and displacement level.

The dynamics of a semi-infinite Euler–Bernoulli beam on unilateral elastic springs is investigated. The mechanical model is governed by a moving-boundary hyperbolic problem, which cannot be solved in closed form. Therefore, we look for approximated solutions following two different approaches. From the one side, approximate analytical solutions are obtained by means of perturbation techniques. On the other side, numerical solutions are determined by a self-made finite element algorithm. The analytical and numerical solutions are compared with each other, and the effects of the problem nonlinearity on the beam motion are analyzed. In particular, the superharmonics oscillations and the resonances are investigated in depth.