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CONTENTS
Volume 70, Number 3, May10 2019
 

Abstract
Expressions for the calculation of ductility index for concrete girders with different ratios of prestressed and classical reinforcement were proposed using load–displacement, load–strain and load–curvature relation. The results of previous experimental static tests of several large-scale concrete girders with different ratio of prestressed and classical reinforcement are briefly presented. Using the proposed expressions, various ductility index of tested girders were calculated and discussed. It was concluded that the ductility of girders decreases approximately linearly by increasing the degree of prestressing. The study presents an expression for the calculation of the average ductility index of classical and prestressed reinforced concrete girders, which are similar to the analysed experimental test girders.

Key Words
concrete; prestressed girders; ductility index; experimental test; analytical expression; load-displacement relation, load-strain relation; load-curvature relation

Address
1Department of Concrete Structures and Bridges, Faculty of Civil Engineering, Architecture and Geodesy,
University of Split, Matice Hrvatske 21000 Split, Croatia
2Department for Mechanics, Materials and Construction, Faculty of Civil Engineering, University of Mostar,
Matice hrvatske b.b. Mostar, Bosnia and Herzegovina
3Department of Concrete Structures and Bridges, Faculty of Civil Engineering, Architecture and Geodesy, U
niversity of Split, Matice Hrvatske 21000 Split, Croatia
4Department for Mechanics, Materials and Construction, Faculty of Civil Engineering, University of Mostar,
Matice hrvatske b.b. Mostar, Bosnia and Herzegovina

Abstract
Using the non-local elasticity theory, Timoshenko beam model is developed to study the non- local buckling of Triple-walled carbon nanotubes (TWCNTs) embedded in an elastic medium under axial compression. The chirality and small scale effects are considered. The effects of the surrounding elastic medium based on a Winkler model and van der Waals\'(vdW) forces between the inner and middle, also between the middle and outer nanotubes are taken into account. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling loads under axial compression are obtained. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed. Furthermore, in order to estimate the impact of elastic medium on the non-local critical buckling load of TWCNTs under axial compression, the use of these findings are important in mechanical design considerations, improve and reinforcement of devices that use carbon nanotubes.

Key Words
triple-walled carbon nanotubes; elastic medium; nonlocal elasticity; chirality; buckling; Timoshenko beam theory

Address
1Département de Génie Civil, Université Ibn Khaldoun Tiaret, BP 78 Zaaroura, Tiaret, Algérie
2Laboratoire de Géomatique et Développement Durable, Université de Tiaret, Algérie

Abstract
This paper intends to introduce a near-tip grid refinement and to explore its usefulness in the crack analysis by the natural element method (NEM). As a sort of local h-refinement in FEM, a NEM grid is locally refined around the crack tip showing the high stress singularity. This local grid refinement is completed in two steps in which grid points are added and Delaunay triangles sharing the crack tip node are divided. A plane-state plate with symmetric edge cracks is simulated to validate the proposed local grid refinement and to examine its usefulness in the crack analysis. The crack analysis is also simulated using a uniform NEM grid for the sake of comparison. The near-tip stress distributions and SIFs that are obtained using a near-tip refined NEM grid are compared with the exact values and those obtained using uniform NEM grid. The convergence rates of global relative error to the total number of grid points between the refined and non-refined NEM grids are also compared.

Key Words
crack analysis; near-tip grid refinement; natural element method; stress intensity factor; near-tip stress distribution; convergence rate

Address
Department of Naval Architecture and Ocean Engineering, Hongik University, Jochiwon, Sejong 30016, Korea

Abstract
Hysteretic energy is defined as energy dissipated through inelastic deformations during a ground motion by the system. It includes frequency content and duration of ground motion as two remarkable parameters, while these characteristics are not seen in displacement spectrum. Since maximum displacement individually cannot be the appropriate criterion for damage assessment, hysteretic energy has been evaluated in this research as a more comprehensive seismic demand parameter. An innovative methodology has been proposed to establish a new equivalent linear model to estimate hysteretic energy spectrum for bilinear SDOF models under two different sets of earthquake excitations. Error minimization has been defined in the space of equivalent linearization concept, which resulted in equivalent damping and equivalent period as representative parameters of the linear model. Nonlinear regression analysis was carried out for predicting these equivalent parameter as a function of ductility. The results also indicate differences between seismic demand characteristics of far-field and near-field ground motions, which are not identified by most of previous equations presented for predicting seismic energy. The main advantage of the proposed model is its independency on parameters related to earthquake and response characteristics, which has led to more efficiency as well as simplicity. The capability of providing a practical energy based seismic performance evaluation is another outstanding feature of the proposed model.

Key Words
linearization; hysteretic energy; seismic demand; equivalent period; equivalent damping; far-field; near-field

Address
1Department of Civil Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
2Structural Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran, Iran

Abstract
Any revision of seismic codes usually demands a higher capacity from structural members, making existing structures unsafe particularly from strength considerations. Retrofitting of capacity deficient members is very suitable for tackling such situations. This paper presents an experimental study on different retrofitting measures adopted for strengthening a series of reinforced concrete (RC) beams. Four identical RC beam specimens were casted, out of which three specimens were strengthened by different schemes (viz., bolted hot rolled flat, bolted cold-formed steel channel, and carbon fibre reinforced polymer (CFRP) laminate, respectively) on their tension face and tested under four-point monotonic loading. This study focuses on the investigation of the flexural behaviour of these retrofitted beams, observed in terms of strength and stiffness. It was concluded that all retrofitting measures improved the structural performance of these beams. However, the cost involved with each strengthening mode was proportional to the improvement in the performance achieved.

Key Words
flexural members; experimental investigation; cold-formed steel; carbon fibre reinforced polymer laminate

Address
1Department of Civil Engineering, Indian Institute of Technology Delhi, New Delhi, India
2Consulting Engineer, Maryland, USA
3Department of Civil Engineering, National Institute of Technology Srinagar, J&K, India

Abstract
Long-span steel suspension bridges develop significant vibrations under the effect of external time-variable loadings because their slenderness. This causes significant stresses variations that could induce fatigue problems in critical components of the bridge. The research outcome presented in this paper includes a fatigue analysis of a long suspension bridge with 3300 meters central suspended span under wind action and train transit. Special focus is made on the counterintuitive interaction effects between train and wind loads in terms of fatigue damage accumulation in the hanger ropes. In fact the coupling of the two actions is shown to have positive effects for some hangers in terms of damage accumulation. Fatigue damage is evaluated using a linear accumulation model (Palmgren-Miner rule), analyses are carried out in time domain by a three-dimensional non-linear finite element model of the bridge. Rational explanation regarding the above-mentioned counterintuitive behavior is given on the basis of the stress time histories obtained for pertinent hangers under the effects of wind and train as acting separately or simultaneously. The interaction between wind and train traffic loads can be critical for a some hanger ropes therefore interaction phenomena within loads should be considered in the design.

Key Words
suspension bridges; fatigue analysis; wind-train interaction; damage accumulation; non-linearity

Address
1Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via Eudossiana 18, Rome, Italy
2Taisei Corporation, Shinjuku Center Building, Nishi Shinjuku 1-25-1, Tokyo, Japan

Abstract
In the present article, cross ply laminated composite plates are considered and a simple sinusoidal shear deformation model is tested for analyzing their flexural, stability and dynamic behaviors. The model contains only four unknown variables that are five in the first order shear deformation theory (FSDT) or other higher order models. The in-plane kinematic utilizes undetermined integral terms to quantitatively express the shear deformation influence. In the proposed theory, the conditions of zero shear stress are respected at bottom and top faces of plates without considering the shear correction coefficient. Equations of motion according to the proposed formulation are deduced by employing the virtual work principle in its dynamic version. The analytical solution is determined via double trigonometric series proposed by Navier. The stresses, displacements, natural frequencies and critical buckling forces computed using present method are compared with other published data where a good agreement between results is demonstrated.

Key Words
shear deformation; flexural, buckling; dynamic; cross-ply laminates; laminated plates

Address
1Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria
2Centre Universitaire Ahmed Zabana de Relizane, Algeria
3Département de Génie Civil, Université Ibn Khaldoun Tiaret, BP 78 Zaaroura, 14000 Tiaret, Algérie
4Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes,
Département de Physique, Université de Sidi Bel Abbés, Algeria
5Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran,
Eastern Province, Saudi Arabia

Abstract
This research focuses on finite element model updating and damage assessment of structures at element level based on global nondestructive test results. For this purpose, an optimization system is generated to minimize the structural dynamic parameters discrepancies between numerical and experimental models. Objective functions are selected based on the square of Euclidean norm error of vibration frequencies and modal assurance criterion of mode shapes. In order to update the finite element model and detect local damages within the structural members, modern optimization techniques is implemented according to the evolutionary algorithms to meet the global optimized solution. Using a simulated numerical example, application of genetic algorithm (GA), particle swarm (PSO) and artificial bee colony (ABC) algorithms are investigated in FE model updating and damage detection problems to consider their accuracy and convergence characteristics. Then, a hybrid multi stage optimization method is presented merging advantages of PSO and ABC methods in finding damage location and extent. The efficiency of the methods have been examined using two simulated numerical examples, a laboratory dynamic test and a high-rise building field ambient vibration test results. The implemented evolutionary updating methods show successful results in accuracy and speed considering the incomplete and noisy experimental measured data.

Key Words
Finite Element Model updating; GA; PSO; ABC; hybrid optimization; damage detection, modal analysis

Address
School of Civil Engineering, College of Engineering, University of Tehran, 16 Azar St, Enghelab Ave., Tehran, Iran

Abstract
In this paper, free vibration of Cooper-Naghdi micro sandwich cylindrical shell with saturated porous core and reinforced carbon nanotube (CNT) piezoelectric composite face sheets is investigated by using first order shear deformation theory (FSDT) and modified couple stress theory (MCST). The sandwich shell is subjected to magneto-thermo-mechanical loadings with temperature dependent material properties. Energy method and Hamilton\'s principle are used for deriving of the motion equations. The equations are solved by Navier\'s method. The results are compared with the obtained results by the other literatures. The effects of various parameters such as saturated porous distribution, geometry parameters, volume fraction and temperature change on the natural frequency of the micro-sandwich cylindrical shell are addressed. The obtained results reveal that the natural frequency of the micro sandwich cylindrical shell increases with increasing of the radius to thickness ratio, Skempton coefficient, the porosity of the core, and decreasing of the length to radius ratio and temperature change.

Key Words
Cooper-Naghdi micro sandwich cylindrical shell; carbon nanotube reinforced piezoelectric composite; first order shear deformation theory; modified couple stress theory; saturated porous distribution; free vibration

Address
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box:87317-53153, Kashan, Iran

Abstract
The paper concerns topology and geometry optimization of statically determinate beams with arbitrary number of supports. The optimization problem is treated as a bi-criteria one, with the objectives of minimizing the absolute maximum bending moment and the maximum deflection for a uniform gravity load. The problem is formulated and solved using the Pareto optimality concept and the lexicographic ordering of the objectives. The non-dominated sorting genetic algorithm NSGA-II and the local search method are used for the optimization in the Pareto sense, whereas the genetic algorithm and the exhaustive search method for the lexicographic optimization. Trade-offs between objectives are examined and sets of Pareto-optimal solutions are provided for different topologies. Lexicographically optimal beams are found assuming that the maximum moment is a more important criterion. Exact formulas for locations and values of the maximum deflection are given for all lexicographically optimal beams of any topology and any number of supports. Topologies with lexicographically optimal geometries are classified into equivalence classes, and specific features of these classes are discussed. A qualitative principle of the division of topologies equivalent in terms of the maximum moment into topologies better and worse in terms of the maximum deflection is found.

Key Words
Pareto optimality; lexicographic ordering; beams; topology and geometry optimization; bending moment; deflection

Address
Faculty of Architecture, Bialystok University of Technology, Oskara Sosnowskiego 11, 15-351 Bialystok, Poland


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