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CONTENTS
Volume 14, Number 3, June 2025
 

Abstract
Current design codes of practice ignore the effect of interaction between primary and secondary systems when addressing the seismic response of coupled structures. The present investigation offers a robust mathematical representation of such interaction through a closed-form calculation of time periods in coupled primary-secondary systems. On this wise, an analytic framework was established to determine the fundamental period of a threedimensional (3D) steel moment-resisting frame structures. The successful verification of the analytic formulation followed using a finite element (FE) modeling approach. Subsequently, a parametric study was carried out to address the effect of number and location of secondary systems, as well as number of frame stories, on the overall seismic response of the coupled system. The mass of secondary system was considered less than 20% of that of the primary system. Based on the FE modeling results, the most significant effect of secondary system on the response of coupled system relates to time period, which should be taken into account in current design procedures. Despite the very low mass of secondary system, time period of the coupled frame changed significantly, when the secondary system was added to primary structure. This causes the amplification of lateral drifts and deformations, leading to structural and non-structural damage, and potential failure. On the contrary, the fundamental period of short-rise frames increased with increasing secondary-to-coupled-system mass ratio. Based on this finding, it is viable to increase the time period of short-rise structures under the effect of secondary system period, and thus improve their seismic performance.

Key Words
coupled system; earthquake excitation; finite-element modeling (FEM); seismic response; steel frame; time period

Address
Omid Fereidooni, Panam Zarfam and Mohammadreza Mansoori: Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

Abstract
This article explores the impact of support conditions on a uniformly loaded FGM beam, focusing on hyperstaticity and material heterogeneity. It presents a mathematical formulation based on elasticity theory, considering edge conditions to predict stress and displacement distribution. Numerical tests validate the influence of these conditions on the FGM beam's supports, resulting in satisfactory resistance and stability. The study also presents numerical tests to validate the results, demonstrating the importance of considering the different parameters of variations in support conditions at the edge.

Key Words
boundary conditions; elastic properties; elasticity solution; functionally graded beams; static analysis

Address
Abdelaziz Hadj Henni: Department of Civil Engineering, Ibn Khaldoun University of Tiaret, Algeria
Tahar Hassaine Daouadji: Department of Civil Engineering, Ibn Khaldoun University of Tiaret, Algeria; Laboratory of Geomatics and Sustainable Development LGéo2D, University of Tiaret, Algeria

Abstract
This research investigates the innovative design of steel fibers and their effects on the soft computing methodologies applied to steel fiber reinforced self-compacting concrete (SFRSCC). The study aims to enhance the mechanical properties and durability of SFRSCC through the strategic integration of steel fibers, utilizing advanced soft computing techniques. The fraction of steel fibers of the SFRSCC is 0.5 vol.%,1.5 vol.% and 2.0 vol.% respectively. In conclusion, the research underscores the potential of SFRSCC as a high-performance material that addresses the challenges faced in contemporary construction. By leveraging innovative design strategies and advanced computational techniques, the study contributes to the ongoing evolution of concrete technology, paving the way for more sustainable and efficient building practices. Future research should continue to explore the longterm durability and environmental impact of SFRSCC, further solidifying its role in the advancement of construction materials.

Key Words
coupled systematic criterion; mechanical performance; self-compacting; steel fiber

Address
C.C. Hung: School of Intelligent Manufacturing and Electrical Engineering, Guangzhou Institute of Science and Technology, Guangzhou 510540, China
Huang Huandi: School of Business, Macau University of Science and Technology, Macau
T. Nguyễn: Ha Tinh University, Dai Nai Ward, Ha Tinh City, Vietnam
C.Y. Hsieh: National Pingtung University Education School,
No.4-18, Minsheng Rd., Pingtung City, Pingtung County 900391, Taiwan

Abstract
This paper examines the dynamic instability of a suspension bridge deck, modeling it as a symmetrically laminated rectangular plate made of composite material, featuring an angular fold and subject to various boundary conditions. To simplify the analysis, the instability of this structure is studied under the effect of a dynamic, nonuniform and periodic uni-axial loading applied along its edges. The equations of motion are formulated using Reissner-Mindlin's first-order shear deformation theory (FSDT) and Hamilton's principle. FSDT is based on five degrees of freedom (DOF) modeling per node within a finite element approach. Structural damping, modeled using the Rayleigh method, is incorporated into the system of equations to assess its influence on instability characteristics. A modal analysis is then performed to decouple the partial differential equations (PDEs) into a Mathieu-Hill system of ordinary differential equations (ODEs), thus reducing the problem size. The dynamic instability zones (DIR) of the plate are identified by applying the Bolotin approach, while the dynamic excitation frequencies are determined by solving an eigenvalue problem. Finally, a parametric analysis is carried out to examine the influence of the various parameters on the lower and upper bounds of the instability zones, as well as on the simple parametric resonance phenomenon of the structure representing the deck.

Key Words
Bolotin approach; dynamic instability; dynamic load; Mathieu-Hill equations; Runge Kutta algorithm; suspension bridge deck

Address
Hafid Mataich: Laboratory of Informatics and Interdisciplinary Physics (LIPI), High Normal School, Sidi Mohamed Ben Abdellah University, 30040 Fez, Morocco

Abstract
This study employs an advanced four-variable plate theory to examine the mechanical bending response of simply supported rectangular metal foam plates. With the rise of composite materials in the aerospace, automotive, and transportation sectors, there is a need for analytical techniques to model their performance in various environments. Functionally graded porous plates (FGPs) are composites with gradual variations in porosity. Nevertheless, few studies have systematically investigated the effects of geometric parameters and mechanical loadings on the mechanical properties of metal foam plates using plate theory. The aim of this study is to shed the light on the elastic bending behavior of imperfect plates under sinusoidal loading by applying a refined plate theory that incorporates both bending and shear components of transverse displacement into the kinematic framework. This formulation simplifies structural analysis by reducing the number of governing equations. Specifically, we analyze a simply supported imperfect metal-foam plate with two distinct porosity levels subjected to a sinusoidally distributed load. The results reveal intricate dependencies between plate geometry, thickness, and deflection behavior, including critical transitions at specific thickness ratios. The refined plate theory closely matches higher-order shear deformation theories, thereby justifying its accuracy and reliability. The findings advance the understanding of metal foam plate mechanics and enhance the design of structures particularly in aerospace and automotive engineering where accurate prediction of plate behavior is essential.

Key Words
geometric parameters; mechanical bending; metal foam plates; refined plate theory; semianalytical approach; sinusoidal loading

Address
Nabil Himeur: Mechanical Engineering Department, Faculty of Science & Technology, University Abbes Laghrour, Khenchela 40000, Algeria; Laboratory of Engineering and Sciences of Advanced Materials (ISMA), Abbes Laghrour University Khenchela, 40004, Algeria
Messaoud Baazouzi: Civil Engineering Department, Faculty of Sciences & Technology, University Abbes Laghrour, Khenchela 40000, Algeria; Civil Engineering Research Laboratory LRGC, Biskra University, 07000 Biskra, Algeria
Khawla Boudiaf: Civil Engineering Department, Faculty of Sciences & Technology, University Abbes Laghrour, Khenchela 40000, Algeria; Civil Engineering Research Laboratory LRGC, Biskra University, 07000 Biskra, Algeria
Mohamed Tabet: Civil Engineering Department, Faculty of Sciences & Technology, University Abbes Laghrour, Khenchela 40000, Algeria; Civil Engineering Research Laboratory LRGC, Biskra University, 07000 Biskra, Algeria
Dalila Kamli: Laboratory of Electrochemistry, Molecular Engineering and Redox Catalysis (LEIMCR), Department of Basic Technology Education, Faculty of Technology, Ferhat Abbas University, Sétif-1, Algeria; Department of Material Sciences, Faculty of Sciences & Technology, University of Khenchela, Algeria
Abderrahmane Menasria: Civil Engineering Department, Faculty of Sciences & Technology, University Abbes Laghrour, Khenchela 40000, Algeria; Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, Djillali Liabes University, Sidi Bel Abbes 22000, Algeria
Abdelhakim Bouhadra: Civil Engineering Department, Faculty of Sciences & Technology, University Abbes Laghrour, Khenchela 40000, Algeria; Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, Djillali Liabes University, Sidi Bel Abbes 22000, Algeria

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