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Volume 3, Number 3, July 2018

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

Key Words
zig-zag theory; analytical solution; levy-type; free vibration; sandwich plate; composite plate

Department of Mechanical Engineering, Indian Institute of Technology Guwahati,
Guwahati-781039, Assam, India

Conventional seismic design of concentrically braced frame (CBF) structures suggests that the gusset plate connecting a steel brace to beams and/or columns should be designed as non-dissipative in earthquakes, while the steel brace members should be designed as dissipative elements. These design intentions lead to thicker and larger gusset plates in design on one hand and a potentially under-rated contribution of gusset plates in design, on the other hand. In contrast, research has shown that compact and thinner gusset plates designed in accordance with the elliptical clearance method rather than the conventional standard linear clearance method can enhance system ductility and energy dissipation capacity in concentrically braced steel frames. In order to assess the two design methods, six cyclic push-over tests on full scale models of concentric braced steel frame structures were conducted. Furthermore, a 3D finite element (FE) shell model, incorporating state-of-the-art tools and techniques in numerical simulation, was developed that successfully replicates the response of gusset plate and bracing members under fully reversed cyclic axial loading. Direct measurements from strain gauges applied to the physical models were used primarily to validate FE models, while comparisons of hysteresis load-displacement loops from physical and numerical models were used to highlight the overall performance of the FE models. The study shows the two design methods attain structural response as per the design intentions; however, the elliptical clearance method has a superiority over the standard linear method as a fact of improving detailing of the gusset plates, enhancing resisting capacity and improving deformability of a CBF structure. Considerations were proposed for improvement of guidelines for detailing gusset plates and bracing members in CBF structures.

Key Words
seismic design; concentrically braced frames; steel structures; earthquake engineering; gusset plates; steel hollow sections; finite element modelling

M.S. Hassan, S. Salawdeh, and J. Goggins:
1. Civil Engineering, School of Engineering, National University of Ireland Galway, Ireland
2. MaREI Centre for Marine and Renewable Energy Ireland, Ryan Institute, National University of Ireland, Galway, Ireland
A. Hunt: AECOM, St Albans, United Kingdom
B.M. Broderick: Department of Civil, Structural & Environmental Engineering, Trinity College Dublin, Ireland

180 different 2D numerical analyses have been carried out to estimate the factor of safety (FOS) for rooted slopes. Four different types of vegetated coverage and a variety of slope geometry considering three types of soil have been evaluated in this study. The highly influenced parameters on the slope\'s FOS are determined. They have been chosen as the input parameters for developing a new practical relationship to estimate the FOS with an emphasis on the roots effects. The dependency of sliding mode and shape considering the soil and roots-type has been evaluated by using the numerical finite element model. It is observed that the inclination and height of the slope and the coverage type are the most important effective factors in FOS. While the soil strength parameters and its physical properties would be considered as the second major group that affects the FOS. Achieved results from the developed relationship have shown the acceptable estimation for the roots slope. The extracted R square from the proposed relationship considering nonlinear estimation has been achieved up to 0.85. As a further cross check, the achieved R square from a multi-layer neural network has also been observed to be around 0.92. The numerical verification considering different scenarios has been done in the current evaluation.

Key Words
rooted slope; numerical; relationship; factor of safety

Pouyan Abbasi Maedeh, Wei Wu, Madhu Sudan Acharya: University of Natural Resources and Life Sciences, Institue of Geotechnical Engineering, Vienna, Austria
António Viana da Fonseca: University of Porto, Faculty of civil engineering, Porto, Portugal
Kourosh Ghaffari Irdmoosa: Kharazmi University, Faculty of engineering, Iran, Tehran
Ehsan Bodaghi:Islamic Azad University, South Branch, Tehran, Iran

The use of optimum content of supplementary cementing materials (SCMs) such as limestone filler (LF) to blend with Portland cement has been resulted in many environmental and technical advantages, such as increase in physical properties, enhancement of sustainability in concrete industry and reducing CO2 emission are well known. Artificial neural networks (ANNs) have been already applied in civil engineering to solve a wide variety of problems such as the prediction of concrete compressive strength. The feed forward back propagation (FFBP) algorithm and Tan-sigmoid transfer function were used for the ANNs training in this study. The training, testing and validation of data during the backpropagation training process yielded good correlations exceeding 97%. A parametric study was conducted to study the sensitivity of the developed model to certain essential parameters affecting the compressive strength of concrete. The effects and benefits of limestone filler on hardened properties of the concrete such as compressive strength were well established endorsing previous results in the literature. The results of this study revealed that the proposed ANNs model showed a high performance as a feasible and highly efficient tool for simulating the LF concrete compressive strength prediction.

Key Words
concrete, limestone filler, compressive strength, prediction, artificial neural networks

Hocine Ayat, Yasmina Kellouche, Mohamed Ghrici and Bakhta Boukhatem: Geomaterials Laboratory, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
Bakhta Boukhatem: Department of Civil Engineering, University of Sherbrooke, Sherbrooke, Canada

This article presents a semi-analytical solution for an exponentially graded piezoelectric hollow sphere. The sphere interacts with electric displacement, elastic deformations, electric potentials, magneto-thermo-elasticity, and hygrothermal influences. The hollow sphere may be standing under both mechanical and electric potentials. Electro-magneto-elastic behavior of magnetic field vector can be described in the hollow sphere. All material, thermal and magnetic properties of hollow sphere are supposed to be graded in radial direction. A semi-analytical technique is improved to deduce all fields in which different boundary conditions for radial stress and electric potential are presented. Numerical examples for radial displacement, radial and hoop stresses, and electric potential are investigated. The influence of many parameters is studied. It is seen that the gradation of all material, thermal and magnetic properties has particular effectiveness in many applications of modern technology.

Key Words
exponentially graded material; semi-analytical technique; perturbation of magnetic field; hygrothermal effect; piezoelectric materials

M.N.M. Allam: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
R. Tantawy: Department of Mathematics, Faculty of Science, Damietta University, Damietta 34517, Egypt
A.M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

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