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In this study, the influence of concentrated damage on the stability of beams under static loads is investigated according to a co-rotational-based large displacement approach. Well-known benchmark beam-like structures have been considered under different loading conditions and damage scenarios. The concentrated damage has been modelled by means of a cross section reduction of a beam element, following a strategy already adopted in the literature. The results have been expressed in terms of buckling loads and post-buckling responses for different damage scenarios associated with a concentrated damage characterized by different positions, intensities, and extensions.

A procedure tailored for a practical calibration of partial safety factors (PSF) related to input material properties is presented. The methodology addresses the propagation of material and model uncertainty through a FORM-based calibration, resulting in a noteworthy reduction in computation time compared to full probabilistic approaches. The novelty lies on the introduction of the Star Design with Central Point (SDCP) method for the computation of sensitivity coefficients and corresponding partial safety factors for material uncertainty. A calibration example is reported with reference to unreinforced masonry structures under out-of-plane failure. The effect of considering different geometries, failure modes, and modelling approaches is explored. A comparative analysis involving different approaches to propagate uncertainties emphasize the promising potential of the proposed procedure.

This paper presents the numerical evaluation of the seismic response of a masonry cross vault using the Discrete Macro-Element Method (DMEM). The case study corresponded to a full-scale unstrengthened cross vault that was experimentally investigated within the scope of the SERA Project — Seismic Response of Masonry Cross Vaults: Shaking table tests and numerical validations. The cross vault was subjected to repeated shaking table and dynamic identification tests until reaching significant damage. The numerical simulations involved the calibration of the Young's modulus of the masonry material aiming at reproducing the cross vault's experimental natural frequencies and mode shapes. The comparison of frequencies was carried out by estimating the difference between experimental and numerical results, whereas the correspondence between mode shapes was studied using the Modal Assurance Criterion. Subsequently, a sensitivity analysis was performed to identify the influence of nonlinear properties on the seismic response of the cross vault (displacement and acceleration time histories and failure mechanism). The accuracy of the numerical time histories was evaluated by estimating magnitude and phase discrepancies. The results aimed at demonstrating the applicability of the DMEM for assessing the seismic response of masonry cross vaults with an acceptable degree of accuracy and low computational cost. [ABSTRACT FROM AUTHOR]

The dynamic stiffness method is developed to analyze the natural vibration characteristics of functionally graded beams, where material properties change continuously across the beam thickness following a symmetric law distribution. The governing equations of motion and associated natural boundary conditions for free vibration analysis are derived using Hamilton's principle and closed-form exact solutions are obtained for both Euler–Bernoulli and Timoshenko beam models. The dynamic stiffness matrix, which governs the relationship between force and displacements at the beam ends, is determined. Using the Wittrick–Williams algorithm, the dynamic stiffness matrix is employed to compute natural frequencies and mode shapes. The proposed procedure is validated by comparing the obtained frequencies with those given by approximated well-known formulas. Finally, a parametric investigation is conducted by varying the geometry of the structure and the characteristic mechanical parameters of the functionally graded material. [ABSTRACT FROM AUTHOR]