The behavior of steel frame buildings under progressive collapse conditions depends on a combination of several parameters, including the interplay between different collapse resistance mechanisms that are mobilized in different structural components. Previous studies have shown that the extent to which these mechanisms may contribute to progressive collapse resistance depends on the ability of the beam-column connections to undergo large inelastic deformations prior to reaching their deformation capacity limits. For this reason, and due to the important role of their flexural strength and tying capacity in the development of essential collapse resistance mechanisms, the response of beam-column connections is one of the most important features of progressive collapse performance. Based on the knowledge gained through previous studies on the mechanics of this problem, the role of these connections are critically reviewed in this paper by examining the results of several experimental studies that have been conducted during the past decade. The factors that may adversely affect progressive collapse resistance–such as the failure modes of certain connection types–are evaluated, and novel approaches to limiting these factors, which are currently under development, are reviewed. The assessment of these parameters leads to useful conclusions of practical significance while highlighting the aspects of these problems that need further study and understanding.

The main objective of this paper is to establish a complete analytical solution concerning the linear pressure distribution under rigid rectangular spread footings. An eccentricity diagram is developed to map the unique footing deformations and compression zones in each one of five distinct regions. For each region, the linear soil pressure, neutral axis position, and pressure values at the four corners are expressed in closed forms. The accuracy and consistency of the explicit expressions are verified by presenting several special boundary cases, whereas the physical interpretation is brought out by analyzing the eccentricity diagram. A generic nomogram providing the maximum soil pressure is also formed to promote efficient structural footing design. The developed analytical formulas for responses and resultants enable algorithmic implications without iterations and offer high computational efficiency. Proper examples, generated via developed computer software, exhibit how the theoretical content of this article is applied in practice. The software enables three-dimensional (3D) viewing of the deformed and undeformed physical and mathematical model of the structure, allowing detailed visual inspection of the results.

This paper examines and provides a robust solution to the problem of yield and failure curvatures of reinforced concrete (RC) cross-sections, taking into account cracking. At the same time, it calculates the corresponding necessary reinforcement or the moment of resistance in both yield and failure limit states. Computationally, the problem of determining the actual curvatures is reduced to the bending design problem of the cross-section in the yield and failure limit states. This study shows the researcher and the designer how to systematically calculate the strains for different concrete and steel grades and for standard or random cross-sections. This complex process is quite necessary to determine the respective curvatures. The main concept is presented with an emphasis on the “solution regions” as well as the critical cases of the “asymptotic regions”, both in yield and failure limit states. Our wide-ranging research on RC element design under biaxial bending with axial force for both yield and failure limit states has been completed and validated via sophisticated algorithms and is available for publication.

The emergence of the use of mechanical metamaterials for vibration suppression and the creation of frequency gaps in structures require an understanding of the fundament underlying dynamics partial differential equations coupled to ordinary differential equations. Essentially periodic structures consist of a distributed parameter structure connected (embedded) to a series of spring-mass-dampers. Such systems in the past have been studied as combined dynamical systems. This work deals with the modal analysis of non-conservative combined dynamic systems formed by assembling distributed parameter structures and linear, viscously damped, lumped parameter oscillators. The mathematical model of the forced response of such dynamic systems is presented via differential operators. The related non-linear eigenproblem is formulated next and a proper solution is provided. Furthermore, the orthogonality of the eigenfunctions is studied and the completeness of the generated solution space is verified. Coupled modal coordinate differential equations result through modal analysis, thus revealing the non-proportional damping configuration, while the proportional damping conditions are also derived and discussed. The theory is applied to non-conservative Euler–Bernoulli beams subject to different types of boundary conditions and coupled to linear, viscously damped oscillators. A numerical example yields interesting conclusions about the non-proportionality and the applicability of the associated methods to solving the coupled differential equations.

The assessment methods for estimating the behavior of the complex mechanics of reinforced concrete (RC) structural elements were primarily based on experimental investigation, followed by collective evaluation of experimental databases from the available literature. There is still a lot of uncertainty in relation to the strength and deformability criteria that have been derived from tests due to the differences in the experimental test setups of the individual research studies that are being fed into the databases used to derive predictive models. This research work focuses on structural elements that exhibit pronounced strength degradation with plastic deformation and brittle failure characteristics. The study’s focus is on evaluating existing models that predict the shear strength of RC columns, which take into account important factors including the structural element’s ductility and axial load, as well as the contributions of specific resistance mechanisms like that of concrete, transverse, and longitudinal reinforcement. Significantly improved predictive models are proposed herein through the implementation of machine learning (ML) algorithms on refined datasets. Three ML models, LINREG, POLYREG-HYT, and XGBoost-HYT-CV, were used to develop different predictive models that were able to compute the shear strength of RC columns. According to the numerical findings, POLYREG-HYT and XGBoost-HYT-CV derived models outperformed other ML models in predicting the shear strength of rectangular RC columns with the correlation coefficient having a value R greater than 99% and minimal errors. It was also found that the newly proposed predictive model derived a 2-fold improvement in terms of the correlation coefficient compared to best available equation in the international literature.

The behaviour of steel frame buildings under progressive collapse conditions depends on a combination of several parameters including the interplay between different collapse resistance mechanisms mobilized in different structural components. Previous studies have shown that the extent to which these mechanisms may contribute to progressive collapse resistance depends on the ability of the beam-column connections to undergo large inelastic deformations prior to reaching their deformation capacity limits. For this reason, and due to the important role of their flexural strength and tying capacity in the development of essential collapse resistance mechanisms, the response of beam-column connections is one of the most important features of progressive collapse performance. Based on the knowledge gained through previous studies on the mechanics of the problem, the role of the connections is critically reviewed by examining the results of several experimental studies conducted during the past decade. The factors that may adversely affect progressive collapse resistance – such as failure modes of certain connection types – are evaluated, and novel approaches of limiting these factors which are currently under development are reviewed. The assessment of these parameters leads to useful conclusions of practical significance, while highlighting the aspects of the problem that need further study and understanding.