This paper derives an original finite element for the static bending analysis of a transversely cracked uniform beam resting on a two-parametric elastic foundation. In the simplified computational model based on the Euler–Bernoulli theory of small displacements, the crack is represented by a linear rotational spring connecting two elastic members. The derivations of approximate transverse displacement functions, stiffness matrix coefficients, and the load vector for a linearly distributed load along the entire beam element are based on novel cubic polynomial interpolation functions, including the second soil parameter. Moreover, all derived expressions are obtained in closed forms, which allow easy implementation in existing finite element software. Two numerical examples are presented in order to substantiate the discussed approach. They cover both possible analytical solution forms that may occur (depending on the problem parameters) from the same governing differential equation of the considered problem. Therefore, several response parameters are studied for each example (with additional emphasis on their convergence) and compared with the corresponding analytical solution, thus proving the quality of the obtained finite element.

In regions exposed to floods followed by cold weather, brick masonry as a structural basis of the building envelope can be damaged due to the accompanying phenomenon of freezing and thawing. The main purpose of the article is the development of a mathematical model able to predict the chosen mechanical parameters and damage index of brick wallets for a given number of freeze-thaw cycles. For this, a statistical model derived from experimental data is used. As a result, regression curves for Young’s modulus and ductility for two types of mortar are obtained. Furthermore, fragility curves for ductility and also the damage index, which is based on displacement ductility, are presented. The obtained results enable probabilistic risk assessments in the case of deteriorated ductility and increased damage on brick masonry due to freeze–thaw cycles.

This paper focuses on identifying key reasons for the damage of the cylindrical masonry shell structure in St. Jacob`s church in Dolenja Trebuša, Slovenia. Typical damage patterns which can be formed in shell structures and may affect the load bearing capacity are outlined. Several stress states (membrane, bending and also combined stress state) that can occur in the shell structure are described. Load cases such as the vertical displacement of the support structure, temperature loading, weight of maintenance team and also seismic loading are taken into account in order to identify the actual cause for the registered crack pattern in the shell structure. Analysis of the shell structure is performed using the SAP2000 structural software. Based on the obtained results, which highlighted key reasons for registered damage, the monitoring of cracks is recommended in the first phase, and, in continuation, the most appropriate repair and strengthening measures are proposed.