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CONTENTS
Volume 77, Number 5, March10 2021
 

Abstract
The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

Key Words
torsional waves; bi-layered hollow cylinder; wave dispersion; inhomogeneous initial stresses; cut-off wavelength; cut-off frequency

Address
Surkay D. Akbarov: Department of Mechanical Engineering, Faculty of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, 34349, Besiktas, Istanbul, Turkey; Institute of Mathematics and Mechanics of Azerbaijan, National Academy of Sciences, 37011, Baku, Azerbaijan
Emin T. Bagirov: Institute of Mathematics and Mechanics of Azerbaijan, National Academy of Sciences, 37011, Baku, Azerbaijan

Abstract
Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bidimensional functionally graded beams.

Key Words
bi-dimensional; continuous elements method; free vibration ; functionally graded beam

Address
Abdellatif Selmi: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 16273, Saudi Arabia; Ecole Nationale d'Ingénieurs de Tunis (ENIT), Civil Engineering Laboratory. B.P. 37, Le belvédère 1002, Tunis, Tunisia

Abstract
To study the vibration characteristics of a high-speed railway continuous girder bridge-track coupling system (HSRCBT), a coupling vibration analysis model of an m-span continuous girder bridge-subgrade-track system with n-span approach bridge was established. The model was based on the energy and its variational method, where both the interlaminar slip and shear deformation effects were considered. In addition, the free vibration equations and natural boundary conditions of the HSRCBT were derived. Further, according to the coordination principle of deformation and mechanics, an analytical method for calculating the natural vibration frequencies of the HSRCBT was obtained. Three typical bridge-subgrade-track coupling systems of high-speed railway were taken and the results of finite element analysis were compared to those of the analytical method. The errors between the simulation results and calculated values of the analytical method were less than 3%, thus verifying the analytical method proposed in this paper. Finally, the analytical method was used to investigate the influence of the number of the approach bridge spans and the interlaminar stiffness on the natural vibration characteristics of the HSRCBT based on the degree of sensitivity. The results suggest the approach bridges have a critical number of spans and in general, the precision requirements of the analysis could be met by using 6-span approach bridges. The interlaminar vertical compressive stiffness has very little influence on the low-order natural vibration frequency of HSRCBT, but does have a significant influence on higher-order natural vibration frequency. As the interlaminar vertical compressive stiffness increases, the degree of sensitivity to interlaminar stiffness of each of the HSRCBT natural vibration characteristics decrease and gradually approach zero.

Key Words
high-speed railway; shear deformation; interlaminar slip; degree of sensitivity; approach bridge

Address
Yulin Feng: School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, 330013, China; The State Local Joint Engineering Research Center for Security Technology of Operation Maintenance in Rail Transit Infrastructures, Nanchang 330013, China
Lizhong Jiang, Wangbao Zhou, Yuntai Zhang and Xiang Liu: School of Civil Engineering, Central South University, Changsha, 410075, China; National Engineering Laboratory for High Speed Railway Construction, Changsha, 410075, China

Abstract
In this paper, an enhanced Violation-based Sensitivity analysis and Border-Line Adaptive Sliding Technique (ViS-BLAST) will be utilized for optimization of some well-known structural and mechanical engineering problems. ViS-BLAST has already been introduced by the authors for solving truss optimization problems. For those problems, this method showed a satisfactory enactment both in speed and efficiency. The Enriched ViS-BLAST or EVB is introduced to be vastly applicable to any solvable constrained optimization problem without any specific initialization. It uses one-directional step-wise searching technique and mostly limits exploration to the vicinity of FNF border and does not explore the entire design space. It first enters the feasible region very quickly and keeps the feasibility of solutions. For doing this important, EVB groups variables for specifying the desired searching directions in order to moving toward best solutions out or inside feasible domains. EVB was employed for solving seven numerical engineering design problems. Results show that for problems with tiny or even complex feasible regions with a larger number of highly non-linear constraints, EVB has a better performance compared to some records in the literature. This dominance was evaluated in terms of the feasibility of solutions, the quality of optimum objective values found and the total number of function evaluations performed.

Key Words
constrained optimization; sensitivity analysis; mechanical engineering design; highly non-linear

Address
Babak Dizangian: Department of Civil Engineering, Velayat University, Iranshahr, Iran
Mohammad Reza Ghasemi: Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran

Abstract
The speed of rail vehicles become higher and higher over two decades, and China has unveiled a prototype highspeed train in October 2020 that has been able to reach 400 km/h. At such high speeds, wheel-rail force items that had previously been ignored in common computational model should be reevaluated and reconsidered. Aiming at this problem, a new model for investigating the vehicle-bridge interaction at high moving speed is proposed. Comparing with the common model, the new model was more accurate and applicable, because it additionally considers the second-order pseudo-inertia forces effect and its modeling equilibrium position was based on the initial deformed curve of bridge, which could include the influences of temperature, pre-camber, shrinkage and creep deformation, and pier uneven settlement, etc. Taking 5 km/h as the speed interval, the dynamic responses of the classical vehicle-bridge system in the speed range of 5 km/h to 400 km/h are studied. The results show that ignoring the second-order pseudo-inertia force will underestimate the dynamic response of vehicle-bridge system and make the high-speed railway bridge structure design unsafe.

Key Words
vehicle-bridge interaction; high moving speed; high-speed railway; bridge initial deformation; wheel-rail contact force; peak dynamic response

Address
Hanyun Liu, Yan Han: School of Civil Engineering, Changsha University of Science & Technology, Changsha 410114, China
Zhiwu Yu, Wei Guo: DepartmentSchool of Civil Engineering, Central South University, Changsha 410075, China; National Engineering Laboratory of High-Speed Railway Construction Technology, Changsha 410075, China

Abstract
The paper presents an investigation of the widely varying mechanical performance and behaviour of steel and Glass Fibre Reinforced Polymer (GFRP) reinforced concrete beams using non-destructive techniques of Acoustic Emission (AE) and Digital Image Correlation (DIC) under four-point bending. Laboratory experiments are performed on both differently reinforced concrete beams with 0.33%, 0.52% and 1.11% of tension reinforcement against balanced section. The results show that the ultimate load-carrying capacity increases with an increase in tensile reinforcement in both cases. In addition to that, AE waveform parameters of amplitude and number of AE hits successfully correlates and picks up the divergent mechanism of cracking initiation and progression of failure in steel reinforced and GFRP reinforced concrete beams. AE activity is about 20- 30% more in GFRP-RC beams as compared to steel-RC beams. It was primarily due to the lower modulus of elasticity of GFRP bars leading to much larger ductility and deflections as compared to steel-RC beams. Furthermore, AE XY event plots and longitudinal strain profiles using DIC gives an online and real-time visual display of progressive AE activity and strains respectively to efficaciously depict the crack evolution and their advancement in steel-RC and GFRP-RC beams which show a close matching with the micro-and macro-cracks visually observed in the actual beams at various stages of loading.

Key Words
acoustic emission; AE hits; flexure; image correlation; strains; cracks

Address
Gaurav Sharma, Shruti Sharma: Civil Engineering Department, Thapar Institute of Engineering and Technology, Patiala,147004, India
Sandeep K. Sharma: Mechanical Engineering Department, Thapar Institute of Engineering and Technology, Patiala,147004, India

Abstract
In this study, a new constitutive model has been developed to predict the elastic behavior of plain weave textile composites, using the finite element (FE) method. The geometric conditions and basic assumptions of this model are based on the basics of a continuum theory developed for the plane curved composites. In this model, the mechanical properties of the weave region and pure matrix region is calculated separately and then imported for the FE analysis. This new constitutive model is used to implement the mechanical properties of weave region in the representative volume element (RVE). The constitutive relations are implemented as user-material subroutine code (UMAT) in ABAQUS FE software. The results of FE analysis have been compared with experimental results and other data available in the literature. These comparisons confirmed the capability of the presented model for the prediction of effective elastic properties of plain weave fabric composites.

Key Words
woven composites; mechanical properties; constitutive model; representative volume element; finite element analysis

Address
Amir H. Mazaheri and Fathollah Taheri-behrooz: School of Mechanical Engineering, Iran University of Science and Technology, Tehran,16846-13114, Iran

Abstract
In this article, the role of spans number and length in fire-resistance ratings (FRRs) of fireproofed steel frames are investigated. First, over a span-lengthening scenario, two one- and three-bay frames under the ISO834 fire are examined. It is shown that the FRRs of the frames rely highly on the changes made on their span length. Second, a building designed for three spans number of three, four, and five under natural fire is investigated. The beams are designed for two load-capacity-ratios (LCRs) of optimum and ultimate. The fire curves are determined through a probabilistic-based approach. It is shown that the structural vulnerability vastly increases while the number of spans decreases. The results show that for an optimum LCR, while the five-span frame can meet the required FRR in 87% of the fire scenarios, the four- and three-span frames can meet the required FRR in only 56%, and 50% of the fire scenarios, respectively. For an ultimate LCR, the five-, four- and three-span frames can meet the required FRR in 81%, 50%, and 37.5% of the fire scenarios, respectively. Functional solutions are then proposed to resolve the insufficiencies in the results and to rectify the application of the standard-based FRRs in the cases studied. The study here highlights how employing current standard-based FRRs can endanger structural safety if they are not connected to structural characteristics; a crucial hint specifically for the structural engineering community who may be not well familiar with the fundamentals of performance-based approaches.

Key Words
fire-resistance rating; standard fire; natural fire; load to capacity ratio; steel structures; probabilistic-based

Address
Behrouz Behnam: School of Civil and Environmental Engineering, Amirkabir University of Technology, 424 Hafez Street, Tehran, Iran

Abstract
This paper addresses the efficiency of thermal insulation layers applied to protect structural elements strengthened by fiber-reinforced polymers (FRP) in the case of fire event. The paper presents numerical modeling and nonlinear analysis of reinforced concrete (RC) columns externally strengthened by FRP and protected by thermal insulation layers when subjected to elevated temperature specified by standard fire tests, in order to predict their residual capacity and fire endurance. The adopted numerical approach uses commercial software includes heat transfer, variation of thermal and mechanical properties of concrete, steel reinforcement, FRP and insulation material with elevated temperature. The numerical results show good agreement with published results of full-scale fire tests. A parametric study was conducted to investigate the influence of several variables on the structural response and residual capacity of insulated FRP-confined columns loaded by service loads when exposed to fire. The residual capacity of FRP-confined RC column was affected by concrete grade and insulation material and was shown to improve substantially by increasing the concrete cover and insulation layer thickness. By increasing the VG insulation layer thickness 15, 32, 44, 57 mm, the loss in column capacity after 5 hours of fire was 30%, 13%, 7% and 5%, respectively. The obtained results demonstrate the validity of the presented approach for estimation of fire endurance and residual strength, as an alternative for fire testing, and for design of fire protection layers for FRP-confined RC columns.

Key Words
fiber reinforced polymers; columns; elevated temperature; fire protection; fire resistance; numerical modeling; finite elements; nonlinear analysis

Address
Osama O. El-Mahdy, Gehan A. Hamdy and Mohammed Hisham: Department of Civil Engineering, Faculty of Engineering at Shoubra, Benha University, 108 Shoubra St., Shoubra 11691, Cairo, Egypt

Abstract
Reinforced concrete (RC) beams can be subjected to a complex combination of shear forces (V), torsional moments (T), flexural moments (M) and axial loads (N). This paper proposes a unified approach for the analysis of these elements. An existing model for the analysis of orthogonally reinforced concrete membrane elements subjected to in-plane shear and normal stresses is generalized to apply to the case of beams subjected to the complex loading. The combination of V and T can be critical. Torsion is modelled using the hollow-tube analogy. A direct equation for the calculation of the thickness of the equivalent hollow tube is proposed, and the shear stresses caused by V and T are combined using a simple approach. The development and the evaluation of the model are described. The calculations of the model are compared to experimental data from 350 beams subjected to various combinations of stress-resultants and to the calculations of the ACI and the CSA codes. The proposed model provides the most favorable results. It is also shown that it can accurately model the interaction between V and T. The proposed model provides a unified treatment of shear in beams subjected to complex stress-resultants and in thin membrane elements subjected to in-plane stresses.

Key Words
beams; hollow-tube; thin membranes; reinforced concrete; shear; strength; torsion

Address
Khaldoun N. Rahal: Department of Civil Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

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