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CONTENTS
Volume 61, Number 5, March10 2017
 

Abstract
This paper is a continuation of the investigations started in the paper by Akbarov, S.D., Guliyev, H.H and Yahnioglu, N. (2016) \"Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach\", Structural Engineering and Mechanics, 57(2), 239-263, to the case where the three-layered sphere is a hollow one. Three-dimensional exact field equations of elastodynamics are employed for investigation and the discrete-analytical method is employed for solution of the corresponding eigenvalue problem. The FGM is modelled as inhomogeneous for which the modulus of elasticity, Poison\'s ratio and density vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies are presented and discussed. These results are also compared with the corresponding ones obtained in the previous paper by the authors. In particular, it is established that for certain harmonics and for roots of certain order, the values of the natural frequency obtained for the hollow sphere can be greater (or less) than those obtained for the solid sphere.

Key Words
functionally graded material; three-layered hollow sphere; natural vibration; natural frequencies; torsional oscillation; spheroidal oscillation

Address
Surkay D. Akbarov: Department of Mechanical Engineering, Yildiz Technical University, Yildiz Campus, 34349, Besiktas, Istanbul, Turkey; Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, AZ1141, Baku, Azerbaijan
Hatam H. Guliyev: Institute of Geology and Geophysics of the National Academy of Sciences of Azerbaijan, AZ1073, Baku, Azerbaijan
Nazmiye Yahnioglu: Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, 34220, Esenler Istanbul-Turkey

Abstract
A computing procedure is presented to predict the ultimate behavior of prestressed beams under torsion. This computing procedure is based on an extension of the Variable Angle Truss-Model (VATM) to cover both longitudinal and transversal prestressed beams. Several constitutive relationships are tested to model the behavior of the concrete in compression in the struts and the behavior of the reinforcement in tension (both ordinary and prestress). The theoretical predictions of the maximum torque and corresponding twist are compared with some results from reported tests and with the predictions obtained from some codes of practice. One of the tested combinations of the relationships for the materials was found to give simultaneously the best predictions for the resistance torque and the corresponding twist of prestressed beams under torsion. When compared with the predictions from some codes of practice, the theoretical model which incorporates the referred combination of the relationships provides best values for the torsional strength and leads to more optimized designs.

Key Words
PC beams; torsion; longitudinal and transversal prestress; VATM; stress-strain relationships

Address
Luís F.A. Bernardo and Jorge M.A. Andrade: Department of Civil Engineering and Architecture, Centre of Materials and Building Technologies (C-made),University of Beira Interior, Covilhã, Portugal

Abstract
A high-efficiency simplified modelling approach is proposed for investigating the nonlinear responses of reinforced concrete linings of shield tunnels. Material and geometric nonlinearities are considered in the analysis of the lining structures undergoing large deformation before ultimately losing the load-carrying capacity. A beam-spring element model is developed to capture the force-transfer mechanism between lining segments and radial joints. The developed model is validated by comparing analyzed results to experimental results of a single-ring lining structure under two loading conditions: the ground overloading and the lateral unloading respectively. The results show that the lining structure under the lateral unloading due to excavation on the both sides of the tunnel is more vulnerable compared to the case of ground overloading on the top of the tunnel. A parameter study is conducted and results indicate that the lateral pressure coefficient has the greatest influence on the behaviour of the lining structure.

Key Words
shield tunnel lining; simplified model; radial joint model; nonlinear response

Address
Huiling Zhao: State Key Laboratory for Hazard Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, China; Department of Civil Engineering, Shanghai University, 99 Shangda Road, Shanghai, China
Xian Liu, Yong Yuan: State Key Laboratory for Hazard Reduction in Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, China; Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, China
Yihai Bao: Department of Civil and Environmental Engineering, University of California, Davis, Davis, California, 95616, USA

Abstract
Shear failure of reinforced concrete (RC) beams is a major concern for structural engineers. It has been shown through various studies that the shear strength and ductility of RC beams can be improved by adding steel fibers to the concrete. An accurate model predicting the shear strength of steel fiber reinforced concrete (SFRC) beams will help SFRC to become widely used. An artificial neural network (ANN) model consisting of an input layer, a hidden layer of six neurons and an output layer was developed to predict the shear strength of SFRC slender beams without stirrups, where the input parameters are concrete compressive strength, tensile reinforcement ratio, shear span-to-depth ratio, effective depth, volume fraction of fibers, aspect ratio of fibers and fiber bond factor, and the output is an estimate of shear strength. It is shown that the model is superior to fourteen equations proposed by various researchers in predicting the shear strength of SFRC beams considered in this study and it is verified through a parametric study that the model has a good generalization capability.

Key Words
artificial neural network; steel fiber reinforced concrete; slender beam; shear strength

Address
Riza S.O. Keskin: Department of Civil Engineering, Yildiz Technical University, Istanbul, Turkey

Abstract
Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton\'s principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.

Key Words
free vibrations; piezoelectric; nonlocal elasticity; nanobeam

Address
Abbas Kaghazian, Ali Hajnayeb and Hamidreza Foruzande: Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract
Sets of nonlinear formulations together with an energy-based damage index (DI) are proposed to model the behavior and quantify the damage of the confined and unconfined concretes under monotonic and cyclic loading. The proposed formulations and DI can be employed in numerical simulations to determine the stresses and the damages to the fibers or the layers within the sections of reinforced concrete (RC) components. To verify the proposed formulations, an adaptive finite element computer program was generated to simulate the RC structures subjected to monotonic and cyclic loading. By comparing the simulated and the experimental test results, on both the full-scale structural members and concrete cylindrical samples, the proposed uniaxial behavior modeling formulations for confined and unconfined concretes under monotonic and cyclic loading, based on an iterative process, were accordingly adjusted, and then validated. The proposed formulations have strong mathematical structures and can readily be adapted to achieve a higher degree of precision by improving the relevant coefficients based on more precise tests. To apply the proposed DI, the stress-strain data of concrete elements is required. It can easily be calculated by using the proposed nonlinear constitutive laws for confined and unconfined concretes in this paper.

Key Words
confined/unconfined concrete; monotonic/cyclic loading; damage quantification; numerical modeling

Address
Kabir Sadeghi and Fatemeh Nouban: Civil Engineering Department, Near East University, Near East Boulevard, ZIP: 99138, Nicosia, North Cyprus, via Mersin 10, Turkey

Abstract
Carbon fiber reinforced polymers (CFRPs) have been recently investigated as an alternative material for Geosynthetics to improve soil properties. One of the factors influencing the fiber orientation and mechanical properties of CFRP is the effect of soil overburden pressure. This study investigates the tensile behavior of cast-in-place CFRP. During the curing time of specimens, a wide range of normal stress is applied on specimens sandwiched between the soils. Two different soil types are used to determine the effect of soil grain size on the mechanical properties of CFRP. Specimens are also prepared with different specifications such as curing time and mixing soil in to the epoxy. In this study, tensile tests are conducted to investigate the effect of such parameters on tensile behavior of CFRP. The experimental results indicate that by increasing the normal stress and soil grain size, the ultimate tensile strength and the corresponding strain of CFRP decrease; however, reduction in elastic modulus is not noticeable. It should be noted that, increasing the curing period of epoxy resin and mixing soil in to the epoxy have no significant effect on the tensile properties of CFRP.

Key Words
epoxy resin; geosynthetics; CFRP; soil reinforcement; tensile strength; normal stress

Address
Vahid Toufigh: Department of Civil Engineering, Graduate University of Advanced Technology Kerman, Iran
Meysam Pourabbas Bilondi and Farshid Tohidi: of Civil Engineering, Bahonar University of Kerman, Kerman, Iran

Abstract
To determine the seismic applicability of a long-span railway concrete upper-deck arch bridge with concrete-filled steel-tube (CFST) rigid skeleton ribs, some fundamental principles and seismic approaches for long-span bridges are investigated to update the design methods in the current Code for Seismic Design of Railway Engineering of China. Ductile and mixed isolation design are investigated respectively to compare the structural seismic performances. The flexural moment and plastic rotation demands and capacities are quantified to assess the seismic status of the ductile components. A kind of triple friction pendulum (TFP) system and lead-plug rubber bearing are applied simultaneously to regularize the structural seismic demands. The numerical analysis shows that the current ductile layout with continuous rigid frame approaching spans should be strengthened to satisfy the demands of rare earthquakes. However, the mixed isolation design embodies excellent seismic performances for the continuous girder approaching span of this railway arch bridge.

Key Words
seismic applicability; long-span railway arch bridge; CFST rigid skeleton; ductile design; seismic isolation; triple friction pendulum system; lead-plug rubber bearing

Address
Changjiang Shao, Yongjiu Qian: School of Civil Engineering, Key Laboratory of Ministry of Education of Traffic Tunnel Engineering, Southwest Jiaotong University, Chengdu 610031, China
Jiann-wen Woody Ju: Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095, USA; School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China
Guoqing Han: China Railway Eryuan Engineering Group Co. Ltd, Chengdu 610031, China

Abstract
In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn\'t need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

Key Words
Hamiltonian approach; nonlinear vibration; numerical solution

Address
Mahmoud Bayat: Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University, Roudehen, Iran
Iman Pakar: Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Abstract
The determination of the fundamental period of vibration of a structure is essential to earthquake design. Current codes provide formulas for the approximate estimation of the fundamental period of earthquake-resistant building systems. These formulas are dependent only on the height of the structure or number of storeys without taking into account the presence of infill walls into the structure, despite the fact that infill walls increase the stiffness and mass of the structure leading to significant changes in the fundamental period. Furthermore, such a formulation is overly conservative and unable to account for structures with geometric irregularities. In this study, which comprises the companion paper of previous published research by the authors, the effect of the vertical geometric irregularities on the fundamental periods of masonry infilled structures has been investigated, through a large set of infilled frame structure cases. Based on these results, an attempt to quantify the reduction of the fundamental period due to the vertical geometric irregularities has been made through a proposal of properly reduction factor.

Key Words
fundamental period; infilled frames; masonry; modal analysis; reinforced concrete buildings; vertical setback irregularity

Address
Panagiotis G. Asteris, Filippos Foskolos, Alkis Fotos and Athanasios K. Tsaris: Computational Mechanics Laboratory, School of Pedagogical and Technological Education, Heraklion, GR 14121, Athens, Greece
Constantinos C. Repapis: Department of Civil Engineering, Piraeus University of Applied Sciences, 250 Thivon and Petrou Ralli Str., Aigaleo 122 44, Athens, Greece

Abstract
In this paper, a hybrid seismic response control (HSRC) system was developed to control bridge behavior caused by the seismic load. It was aimed at optimum vibration control, composed of a rubber bearing of passive type and MR-damper of semi-active type. Its mathematical modeling was driven and applied to a bridge model so as to prove its validity. The bridge model was built for the experiment, a two-span bridge of 8.3 meters in length with the HSRC system put up on it. Then, inflicting the EI Centro seismic load on it, shaking table tests were carried out to confirm the system\'s validity. The experiments were conducted under the basic structure state (without an MR-damper applied) first, and then under the state with an MRdamper applied. It was also done under the basic structure state with a reinforced rubber bearing applied, then the passive on/off state of the HSRC system, and finally the semi-active state where the control algorithm was applied to the system. From the experiments, it was observed that pounding rather increased when the MR-damper alone was applied, and also that the application of the HSRC system effectively prevented it from occurring. That is, the experiments showed that the system successfully mitigated structural behavior by 70% against the basic structure state, and, further, when control algorithm is applied for the operation of the MR-damper, relative displacement was found to be effectively mitigated by 80%. As a result, the HSRC system was proven to be effective in mitigating responses of the two-span bridge under seismic load.

Key Words
hybrid seismic response control system; rubber bearing; MR-damper; shaking table test; control algorithm

Address
Gwanghee Heo, Chunggil Kim and Joonryong Jeon: Department of Civil Engineering, Konyang University, 121 Daehak-ro, Nonan, Chungcheongnam 32992, Republic of Korea
Seunggon Jeon, Chinok Lee: Department of Civil Engineering, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea

Abstract
The free transverse vibrations of axially functionally graded (AFG) cantilever beams with concentrated masses attached at different points are studied in this paper. The material properties of the AFG beam, consisting of metal and ceramic, vary continuously in the axial direction according to an established law form. Approximated solutions for the title problem are obtained by means of the Ritz Method. The influence of the material variation on the natural frequencies of vibration of the functionally graded beam is investigated and compared with the influence of the variation of the cross section. The phenomenon of dynamic stiffening of beams can be observed in various situations. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study.

Key Words
vibration of beams; AFG beam; tapered beam; attached masses; Ritz method

Address
Carlos A. Rossit, Diana V. Bambill and Gonzalo J. Gilardi: Department of Engineering, Institute of Applied Mechanics, (IMA), Universidad Nacional del Sur, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Avenida Alem 1253, (8000) Bahía Blanca, Argentina


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