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Volume 28, Number 6, September25 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

Key Words
Ritz method; higher order FEM; rectangular thin plates; rectangular thick plates; free edges; free corners; Levy-type boundary conditions

Faculty of Engineering in Eastern Guilan, University of Guilan, Guilan, Iran.

The paper is devoted to the stability analysis of a simply supported five layer sandwich beam. The beam consists of five layers: two metal faces, the metal foam core and two binding layers between faces and the core. The main goal is to elaborate a mathematical and numerical model of this beam. The beam is subjected to an axial compression. The nonlinear hypothesis of deformation of the cross section of the beam is formulated. Based on the Hamilton's principle the system of four stability equations is obtained. This system is approximately solved. Applying the Bubnov-Galerkin&339;s method gives an ordinary differential equation of motion. The equation is then numerically processed. The equilibrium paths for a static and dynamic load are derived and the influence of the binding layers is considered. The main goal of the paper is an analytical description including the influence of binding layers on stability, especially on critical load, static and dynamic paths. Analytical solutions, in particular mathematical model are verified numerically and the results are compared with those obtained in experiments.

Key Words
five layer beam; binding layers; shear effect; equilibrium paths; critical load

(1) Mikolaj J. Smyczynski:
Institute of Applied Mechanics, Poznan University of Technology, ul. Jana Pawla II 24, 60-965 Poznań Poland;
(2) Ewa Magnucka-Blandzi:
Institute of Mathematics, Poznan University of Technology, ul. Piotrowo 3A, 60-965 Poznań Poland.

This paper highlights results of some experimental work that deals with strengthening of bolted shear joints in thin-walled ferrocement structure where steel wires, bent into U-shape are considered as simple inserts around the bolt hole. The parameters investigated include the number of layers of wire mesh, edge distance of bolt hole, size and location of the inserts. Test results have shown that for small edge distance, failure occurred either in cleavage or shearing mode, and the strength of the joint increased with an increase in the edge distance. This continued up to an upper limit set by either tension or bearing failure. The experimental study further revealed that for a given edge distance the strength of a joint can significantly be enhanced by using U-inserts. The equations developed for predicting joint strength in ferrocement composites can also be modified to include the effects of the inserts with a good level of accuracy.

Key Words
ferrocement; composite structure; bolt; shear joint; strength

(1) M. Ismail, M. Shariati, A.S.M. Abdul Awal:
Faculty of Civil Engineering, Universiti Teknologi Malaysia, Johor Bahru, Malaysia;
(2) M. Shariati:
Faculty of Civil Engineering, University of Tabriz, Tabriz, Iran;
(3) M. Shariati:
Department of Civil Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia;
(4) C.E. Chiong:
Faculty of Civil and Environmental Engineering, Universiti Tun Hussein Onn, Malaysia;
(5) E. Sadeghipour Chahnasir, A. Porbar:
Department of Civil Engineering, Qeshm International Branch, Islamic Azad University, Qeshm, Iran;
(6) A. Heydari:
Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran;
(7) M. Khorami:
Facultad de Arquitectura y Urbanismo, Universidad Tecnologica Equinoccial, Calle Rumipamba s/n y Bourgeois, Quito170508, Ecuador.

An innovative Hybrid Passive Resistive configuration for Truss Girder Frames (HPR-TGFs) is introduced in the present study. The proposed system is principally consisting of Fluid Viscous Dampers (FVDs) and Buckling Restrained Braces (BRBs) as its seismic resistive components. Concurrent utilization of these devices will develop an efficient energy dissipating mechanism which is able to mitigate lateral displacements as well as the base shear, simultaneously. However, under certain circumstances which the presence of FVDs might not be essential, the proposed configuration has the potential to incorporate double BRBs in order to achieve the redundancy of alternative load bearing paths. This study is extending the modern Direct Displacement Based Design (DDBD) procedure as the design methodology for HPR-TGF systems. Based on a series of nonlinear time history analysis, it is demonstrated that the design outcomes are almost identical to the pre-assumed design criteria. This implies that the ultimate characteristics of HPR-TGFs such as lateral stiffness and inter-story drifts are well-proportioned through the proposed design procedure.

Key Words
truss girder frames; hybrid passive resistance; direct displacement based design; energy dissipating devices; V-shaped link; bolted hinges

(1) Amir Hamzeh Shaghaghian, Morteza Raissi Dehkordi:
School of Civil Engineering, Iran University of Science and Technology (IUST), Tehran, Iran;
(2) Mahdi Eghbali:
Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran.

Masonry walls are sometimes removed in buildings to either make new passages or increase the usable space. This may change the loading paths in the structure, and require new beams to transfer the loads which are carried by the masonry walls that are to be removed. One possible method of creating such new beams is to attach steel plates onto part of the existing walls to form a steel plate-masonry composite (SPMC) beam, leading to a new structure with part of the masonry wall supported by a new SPMC beam. This paper presents an experimental investigation into the interaction between the SPMC beam and the masonry wall above. Five SPMC beams supporting a masonry wall were tested to study the influence of parameters including the height-to-span ratio of the masonry wall, height of the beam and thickness of the steel plates. The test results, including failure mode, load-carrying capacity, load-deflection curves and strain distribution, are presented and discussed. It is found that for developing better arching effect in the masonry wall the ratio of the in-plane flexural stiffness of the masonry wall to the flexural stiffness of the SPMC beam must be between 2.8 and 7.1.

Key Words
steel plate-masonry composite (SPMC) beam; masonry wall; arching effect; flexural stiffness; local buckling

(1) Deng-Hu Jing, Ting Wu, Shuang-Yin Cao:
School of Civil Engineering, Southeast University, Nanjing, Jiangsu, 211189, China;
(2) Jian-Fei Chen, Giuseppina Amato:
School of Natural and Built Environment, Queen's University Belfast, Belfast BT9 5AG, UK.

Prior to the introduction of modern seismic guidelines, it was a common practice to provide straight bar anchorage for beam bottom reinforcement of gravity load designed building. Exterior joints with straight bar anchorages for beam bottom reinforcements are susceptible to sudden anchorage failure under load reversals and hence require systematic seismic upgradation. Hence in the present study, an attempt is made to upgrade exterior beam-column sub-assemblage of a three storied gravity load designed (GLD) building with single steel haunch. Analytical formulations are presented for evaluating the haunch forces in single steel haunch retrofit. Influence of parameters that affect the efficacy and effectiveness of the single haunch retrofit are also discussed. The effectiveness of the single haunch retrofit for enhancing seismic performance of GLD beam-column specimen is evaluated through experimental investigation under reverse cyclic loading. The single steel haunch retrofit had succeeded in preventing the anchorage failure of beam bottom bars of GLD specimen, delaying the joint shear damage and partially directing the damage towards the beam. A remarkable improvement in the load carrying capacity of the upgraded GLD beam-column sub-assemblage is observed. Further, a tremendous improvement in the energy dissipation of about 2.63 times that of GLD specimen is observed in the case of upgraded GLD specimen. The study also underlines the efficacy of single steel haunch retrofit for seismic upgradation of deficient GLD structures.

Key Words
gravity load designed; beam-column sub-assemblage; upgradation; steel haunch; energy dissipation; strength and stiffness degradation

(1) CSIR-Structural Engineering Research Centre, Chennai, 600113, Tamil Nadu, India;
(2) Academy of Scientific and Innovative Research (AcSIR), Chennai, 600113, Tamil Nadu, India.

In this study, the semi-analytical finite strip method is adopted to examine the free vibration of cylindrical shells made up of functionally graded material. The properties of functionally graded shells are assumed to be temperature-dependent and vary continuously in the thickness direction according to a simple power law distribution in terms of the volume fraction of ceramic and metal. The material properties of the shells and stiffeners are assumed to be continuously graded in the thickness direction. Theoretical formulations based on the smeared stiffeners technique and the classical shell theory with first-order shear deformation theory which accounts for through thickness shear flexibility are employed. The finite strip method is applied to five different shell theories, namely, Donnell, Reissner, Sanders, Novozhilov, and Teng. The approximate procedure is compared favorably with three-dimensional finite elements. Finally, a detailed numerical study is carried out to bring out the effects of power-law index of the functional graded material, stiffeners, and geometry of the shells on the difference between various shell theories. Finally, the importance of choosing the shell theory in simulating the functionally graded cylindrical shells is addressed.

Key Words
free vibration; shell theories; FGM cylinder; stiffeners; finite strip method

Department of Civil Engineering, Shiraz University of Technology, Shiraz, Iran.

Free axial vibration of axially functionally graded (AFG) nanorods is studied by focusing on the inertia of lateral motions and shear stiffness effects. To this end, Bishop's theory considering the inertia of the lateral motions and shear stiffness effects and the nonlocal theory considering the small scale effect are used. The material properties are assumed to change continuously through the length of the AFG nanorod according to a power-law distribution. Then, nonlocal governing equation of motion and boundary conditions are derived by implementing the Hamilton's principle. The governing equation is solved using the harmonic differential quadrature method (HDQM), After that, the first five axial natural frequencies of the AFG nanorod with clamped-clamped end condition are obtained. In the next step, effects of various parameters like the length of the AFG nanorod, the diameter of the AFG nanorod, material properties, and the nonlocal parameter value on natural frequencies are investigated. Results of the present study can be useful in more accurate design of nano-electro-mechanical systems in which nanotubes are used.

Key Words
nonlocal theory; Bishop's theory; axially functionally graded nanorod; axial vibration; jarmonic differential quadrature method

(1) Reza Nazemnezhad:
School of Engineering, Damghan University, Damghan, Iran;
(2) Kamran Kamali:
Impact Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran;
(3) Kamran Kamali:
Department of Design, Fateh Sanat Kimia Company, Great Industrial Zone, Shiraz, Iran.

Friction Stir Welding (FSW) is a solid-state process, where the objects are joined together without reaching their melting point. It has been shown that this method is a suitable way to join dissimilar aluminium alloys. The current article employed hole drilling technique to measure the residual stress distribution experimentally in different zones of dissimilar aluminium alloys AA6061-T6 and AA7075-T6 Butt welded using FSW. Results are compared with those of similar AA6061-T6 plates joined using a conventional fusion welding method called tungsten inert gas (TIG). Also, the evolution of the residual stresses in the thickness direction was investigated, and it was found that the maximum residual stresses are below the yield strength of the material in the shoulder region. It was also revealed that the longitudinal residual stresses in the joint were much larger than the transverse residual stresses. Meanwhile, Vickers micro hardness measurements were performed in the cross-section of the samples. The largest hardness values were observed in the stir zone (SZ) adjacent to the advancing side whereas low hardness values were measured at the HAZ of both alloys and the SZ adjacent to the retreating side.

Key Words
friction stir weld; TIG welding; residual stress measurement; hole drilling method; AA6061; AA7075; similar and dissimilar butt joints

(1) Fathollah Taheri-Behrooz, Mahmood Maroofi, Vahid Hadizadeh:
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, 16846-13114, Iran;
(2) Mohammad R.M. Aliha:
Welding and Joining Research Centre, School of Industrial Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114, Tehran, Iran.

The purpose of this study is to investigate how a fully restrained bolted beam splice affects the connection behavior as a column-tree connection in steel special moment frames under cyclic loading when located within the plastic hinge zone. The impacts of this attachment in protected zone are observed by using nonlinear finite element analyses. This type of splice connection is designed as slip-critical connection and thereby, the possible effects of slippage of the bolts due to a possible loss of pretension in the bolts are also investigated. The 3D models with solid elements that have been developed includes three types of connections which are the connection having fully restrained beam splice located in the plastic hinge location, the connection having fully restrained beam splice located out of the plastic hinge and the connection without beam splice. All connection models satisfied the requirement for the special moment frame connections providing sufficient flexural resistance, determined at column face stated in AISC 341-16. In the connection model having fully restrained beam splice located in the plastic hinge, due to the pretension loss in the bolts, the friction force on the contact surfaces is exceeded, resulting in a relative slip. The reduction in the energy dissipation capacity of the connection is observed to be insignificant. The possibility of the crack occurrence around the bolt holes closest to the column face is found to be higher for the splice connection within the protected zone.

Key Words
steel moment frames; steel beam-to-column connections; column-tree connection; beam splice; plastic hinge; protected zone; finite element analysis; plastic equivalent strain; rupture index

Department of Civil Engineering, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey.

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