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 article aims to provide an accurate mathematical model with the minimum number of degrees of freedom for describing the floating sleeper phenomenon. This was accomplished using mathematical modeling supported by extensive field measurements of the railway track. Although the observed phenomenon is very complex, the simplified single degree of freedom (SDOF) mathematical model proved accurate enough for its characterization. The progression of the deterioration of the railway track was successfully correlated to changes in the maximal dynamic factor for different types of pulse loading. The results of the presented study might enable the enhanced construction and maintenance of railroads, particularly in karst areas.

In this paper, a new beam Euler–Bernoulli finite element for the transverse static bending analysis of cracked slender strip tapered footings on an elastic two-parameter soil is presented. Standard Hermitian cubic interpolation functions are selected to derive the closed-form expressions of complete stiffness matrix and the load vector. The efficiency of the proposed finite element is verified on an example with several width tapering variations of a simple cracked footing with the results of governing differential equation. Another novelty of this study is improved bending moment functions with included discontinuity conditions at the crack location. These functions now accurately describe the bending moments in the vicinity of the crack of the finite element.

This paper presents a detailed analytical approach for the bending analysis of reinforced concrete beams, integrating both structural mechanics principles and Eurocode 2 provisions. The general analytical expressions derived for the curvature were applied for the transverse displacement analysis of a simply supported reinforced concrete beam under four-point loading, focusing on key limit states: the initiation of cracking, the yielding of tensile reinforcement and the compressive failure of concrete. The displacement’s results were validated through experimental testing, showing a high degree of accuracy in the elastic and crack propagation phases. Deviations in the yielding phase were attributed to the conservative material assumptions within the Eurocode 2 framework, though the analytical model remained reliable overall. To streamline the computational process for more complex structures, a simplified model utilising a non-linear rotational spring was further developed. This model effectively captures the influence of cracking with significantly reduced computational effort, making it suitable for serviceability limit state analyses in complex loading scenarios, such as seismic impacts. The results demonstrate that combining detailed analytical methods with this simplified model provides an efficient and practical solution for the analysis of reinforced concrete beams, balancing precision with computational efficiency.

A new finite element with an additional degree of freedom at the crack location is derived for static bending analysis of a transversely cracked uniform slender beam. In the simplified computational model, which is based on Euler-Bernoulli's theory of small displacements, the crack is represented by a linear rotational spring connecting two elastic parts. The derivation of the transverse displacements, the coefficients of the stiffness matrix as well as the load vector for uniformly distributed load along the whole beam element was based on the utilization of polynomial interpolation functions of the fourth degree and all derived expressions were obtained in the closed form. The novelty of the new model, by comparison to the previously presented simplified finite element models, is that the transverse displacements functions obtained by utilization of the newly presented interpolation functions for the case of uniform continuous transverse load along whole beam element, as well as the functions of the bending moments and transverse forces, are accurate. The values obtained by the simplified model also exhibited good agreement in additional comparison with the results from more demanding and more detailed 2D models.