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Volume 26, Number 4, February25 2018

A novel higher shear deformation theory (HSDT) is proposed for the bending, buckling and free vibration investigations of isotropic and functionally graded (FG) sandwich plates. It contains only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The model accounts for a parabolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral terms. Equations of motion determined in this work are applied for three types of FG structures: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Analytical solutions are given to predict the transverse displacements, stresses, critical buckling forces and natural frequencies of simply supported plates and a comparison study is carried out to demonstrate the accuracy of the proposed model.

Key Words
bending; buckling; vibration; sandwich plate; functionally graded materials; plate theory

(1) Hafida Driz, Mamia Benchohra, Ahmed Bakora, Abdelkader Benachour, Abdelouahed Tounsi, El Abbes Adda Bedia:
Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, 22000 Sidi Bel Abbes, Algeria;
(2) Abdelouahed Tounsi:
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia.

Experiments were performed to explore the hysteretic performance of steel reinforced concrete (SRC) cross-shaped columns. Nine specimens were designed and tested under the combined action of compression, flexure, shear and torsion. Torsion-bending ratio (i.e., 0, 0.14, 0.21) and steel forms (i.e., Solid - web steel, T - shaped steel, Channel steel) were considered in the test. Both failure processes and modes were obtained during the whole loading procedure. Based on experimental data, seismic indexes, such as bearing capacity, ductility and energy dissipation were investigated in detail. Experimental results suggest that depending on the torsion-bending ratio, failure modes of SRC cross-shaped columns are bending failure, flexure-torsion failure and torsion-shear failure. Shear - displacement hysteretic loops are fuller than torque - twist angle hysteretic curves. SRC cross-shaped columns exhibit good ductility and deformation capacity. In the range of test parameters, the existence of torque does not reduce the shear force but it reduces the displacement and bending energy dissipation capacity.What is more, the bending energy dissipation capacity increases with the rising of displacement level, while the torsion energy dissipation capacity decreases.

Key Words
steel reinforced concrete (SRC); cross-shaped column; compress-flexure-shear-torsion; combined action; seismic behavior

(1) Zongping Chen, Xiang Liu:
College of Civil Engineering and Architecture, Guangxi University, 100# east daxue road, Nanning,530004, China;
(2) Zongping Chen:
Key Laboratory of Disaster Prevention and Structure Safety of Chinese Ministry of Education, Guangxi University, 100# east daxue road, Nanning, 530004, China.

Free vibration analysis of a three-layered microbeam including an elastic micro-core and two piezo-magnetic face-sheets resting on Pasternak's foundation are studied in this paper. Strain gradient theory is used for size-dependent modeling of microbeam. In addition, three-unknown shear and normal deformations theory is employed for description of displacement field. Hamilton's principle is used for derivation of the governing equations of motion in electro-magneto-mechanical loads. Three micro-length-scale parameters based on strain gradient theory are employed for prediction of vibrational characteristics of structure in micro-scale. The results show that increase of three micro-length-scale parameters leads to significant increase of three natural frequencies especially for increase of second micro-length-scale parameter. This result is according to this fact that stiffness of a micro-scale structure is increased with increase of micro-length-scale parameters.

Key Words
free vibration analysis; strain gradient theory; micro-length-scale parameters; three unknown shear and normal deformation theory; natural frequencies

(1) Mohammad Arefi:
Faculty of Mechanical Engineering, Department of Solid Mechanics, University of Kashan, Kashan 87317-51167, Iran;
(2) Ashraf M. Zenkour:
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
(3) Ashraf M. Zenkour:
Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt.

This paper presents experimental and numerical study on buckling behaviors and hysteretic performance of Class 1 H-shaped steel beam subjected to cyclic pure bending within the scope of ultra-low cycle fatigue (ULCF). A loading device was designed to achieve the pure bending loading condition and 4 H-shaped specimens with a small width-to-thickness ratio were tested under 4 different loading histories. The emphasis of this work is on the impacts induced by local buckling and subsequent ductile fracture. The experimental and numerical results indicate that the specimen failure is mainly induced by elasto-plastic local buckling, and is closely correlated with the plastic straining history. Compared with monotonic loading, the elasto-plastic local buckling can occur at a much smaller displacement amplitude due to a number of preceding plastic reversals with relative small strain amplitudes, which is mainly correlated with decreasing tangent modulus of the material under cyclic straining. Ductile fracture is found to be a secondary factor leading to deterioration of the load-carrying capacity. In addition, a new ULCF life evaluation method is proposed for the specimens using the concept of energy decomposition, where the cumulative plastic energy is classified into two categories as isotropic hardening and kinematic hardening correlated. A linear correlation between the two energies is found and formulated, which compares well with the experimental results.

Key Words
ultra-low cycle fatigue; local buckling; ductile fracture; pure bending; H-shaped beam

(1) Xianzhong Zhao, Yafeng Tian, Tao Zhang:
Deparment of Structural Engineering, Tongji University, Shanghai, 200092, China;
(2) Liang-Jiu Jia:
Research Institute of Structural Engineering and Disaster Reduction, Tongji University, Shanghai, 200092, China.

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

Key Words
non-linear vibration; analytical solution; beam vibration; fourth-order Runge-Kutta method

(1) I. Pakar:
Young Researchers and Elite club, Mashhad Branch, Islamic Azad University, Mashhad, Iran;
(2) M. Bayat:
Young Researchers and Elite Club, Roudehen Branch, Islamic Azad University, Roudehen, Iran;
(3) L. Cveticanin:
Faculty of Technical Sciences, Novi Sad, University of Novi Sad, Novi Sad, Serbia;
(4) L. Cveticanin:
Banki Donat Faculty of Mechanical and Security Engineering, Obuda University, Budapest, Hungary.

The bolted end-plate beam-column connections have been widely used in steel structure and composite structure because of its excellent seismic performance. In this paper, the end-plate bolted connection is applied in the concrete structure, A new-type of fabricated beam-column connections with end-plates is presented, and steel plate hoop is used to replace stirrups in the node core area. To study the seismic behavior of the joint, seven specimens are tested by pseudo-static test. The experimental results show that the new type of assembly node has good ductility and energy dissipation capacity. Besides, under the restraint effect of the high-strength stirrup, the width of the web crack is effectively controlled. In addition, based on the analysis of the factors affecting the shear capacity of the node core area, the formula of shear capacity of the core area of the node is proposed, and the theoretical values of the formula are consistent with the experimental value.

Key Words
bolted end-plate connection; prefabricated joint; seismic behavior; joint core zone; shear capacity

School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, P.R. China.

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

Key Words
free vibration; higher-order theory; spline; composite plates; cross-ply

(1) Saira Javed, K.K. Viswanathan, M.D. Nurul Izyan, Z.A. Aziz:
UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Ibnu Sina Institiute for Scientific & Industrial Research, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia;
(2) K.K. Viswanathan:
Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box 27235, Safat 13133, Kuwait;
(3) J.H. Lee:
Department of Naval Architecture & Ocean Engineering, Inha University, 100 inharo, Nam-gu Incheon 22212, South Korea.

In this paper, a hollow steel tube (HST) shear connector is proposed for use in a slim-floor system. The HST welded to a perforated steel beam web and embedded in concrete slab. A total of 10 push-out tests were conducted under static loading to investigate the mechanical behavior of the proposed HST connector. The variables were the shapes (circular, square and rectangular) and sizes of hollow steel tubes, and the compressive strength of the concrete. The failure mode was recorded as: concrete slab compressive failure under the steel tube and concrete tensile splitting failure, where no failure occurred in the HST. Test results show that the square shape HST in filled via concrete strength 40 MPa carried the highest shear load value, showing three times more than the reference specimens. It also recorded less slip behavior, and less compressive failure mode in concrete underneath the square hollow connector in comparison with the circular and rectangular HST connectors in both concrete strengths. The rectangular HST shows a 20% higher shear resistance with a longer width in the load direction in comparison with that in the smaller dimension. The energy absorption capacity values showed 23% and 18% improvements with the square HST rather than a headed shear stud when embedded in concrete strengths of 25 MPa and 40 MPa, respectively. Moreover, an analytical method was proposed and predicts the shear resistance of the HST shear connectors with a standard deviation of 0.14 considering the shape and size of the connectors.

Key Words
slim-floor; hollow steel tube; shear connector; push-out test; energy absorption capacity

(1) Emad Hosseinpour, Shahrizan Baharom, Wan Hamidon W. Badaruzzaman:
Department of Civil and Structural Engineering, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, Bangi, Selangor, 43600, Malaysia;
(2) Mahdi Shariati, Abdolrahim Jalali:
Faculty of Civil Engineering, University of Tabriz, Bahman Blvd., Tabriz, 5166616471, Iran.

Concrete-filled steel tubular (CFT) columns are commonly used in engineering structures and always subjected to torsion in practice. This paper is thus devoted to investigate the mechanical behavior of circular CFT columns under pure torsion.3D finite element models based on reasonable material constitutive relation were established for analyzing the load-strain (T-–

Key Words
concrete-filled steel tube (CFT); pure torsion; finite element; ultimate bearing capacity; confinement effect

(1) Fa-xing Ding, Qiang Fu, Bing Wen, Qi-shi Zhou:
School of Civil Engineering, Central South University, Changsha 410075, P.R. China;
(2) Xue-mei Liu:
School of Civil Engineering and Built Environment, Queensland University of Technology, Brisbane, QLD 4001, Australia.

In this article, static, buckling and free vibration analyses of a sinusoidal micro composite beam reinforced by single-walled carbon nanotubes (SWCNTs) with considering temperature-dependent material properties embedded in an elastic medium in the presence of magnetic field under transverse uniform load are presented. This system is used at micro or sub micro scales to enhance the stiffness of micro composite structures such as bar, beam, plate and shell. In the present work, the size dependent effects based on surface stress effect and modified strain gradient theory (MSGT) are considered. The generalized rule of mixture is employed to predict temperature-dependent mechanical and thermal properties of micro composite beam. Then, the governing equations of motions are derived using Hamilton's principle and energy method. Numerical results are presented to investigate the influences of material length scale parameters, elastic foundation, composite fiber angle, magnetic intensity, temperature changes and carbon nanotubes volume fraction on the bending, buckling and free vibration behaviors of micro composite beam. There is a good agreement between the obtained results by this research and the literature results. The obtained results of this study demonstrate that the magnetic intensity, temperature changes, and two parameters elastic foundations have important effects on micro composite stiffness, while the magnetic field has greater effects on the bending, buckling and free vibration responses of micro composite beams. Moreover, it is shown that the effects of surface layers are important, and observed that the changes of carbon nanotubes volume fraction, beam length-to-thickness ratio and material length scale parameter have noticeable effects on the maximum deflection, critical buckling load and natural frequencies of micro composite beams.

Key Words
static; buckling; vibration; micro composite beam; surface effect; magnetic and thermal fields

(1) Mehdi Mohammadimehr, Mojtaba Mehrabi, Hasan Hadizadeh, Hossein Hadizadeh:
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box 87317-53153, Kashan, Iran;
(2) Hasan Hadizadeh, Hossein Hadizadeh:
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Tehran, Tehran, Iran.

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