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CONTENTS
Volume 21, Number 6, December20 2005
 

Abstract
A direct transfer substructure method is presented in this paper for analyzing the dynamic characteristics and the seismic random responses of a series reactor. This method combines the concept of FRF (frequency response function) and the transfer matrix algorithm with the substructure approach. The inner degrees of freedom of each substructure are eliminated in the process of reconstruction and the computation cost is reduced greatly. With the convenient solution procedure, the dynamic characteristics analysis of the structure is valid and efficient. Associated with the pseudo excitation algorithm, the direct transfer substructure method is applied to investigating the seismic random responses of the series reactor. The numerical results demonstrate that the presented method is efficient and practicable in engineering. Finally, a precise time integration method is employed in performing a time-history analysis on the series reactor under El Centro and Taft earthquake waves.

Key Words
earthquake; seismic; substructure; random response; dynamic characteristics.

Address
Dept. of Engineering Mechanics, Sch. of Architectural Engineering & Mechanics, Xi?n Jiaotong University, Xi?n, 710049, P. R. China

Abstract
The possibility of detecting a crack in L-shaped pipes filled with fluid based on measurement of transverse natural frequencies is examined. The problem is solved by representing the crack by a massless rotational spring, simulating the out-of-plane transverse vibration only without solving the coupled torsional vibration and using the transfer matrix method for solution of the governing equation. The theoretical solutions are verified by experiments. The cracks considered are external, circumferentially oriented and have straight front. Pipes made of aluminium and mild steel are tested with water as internal fluid. Crack size to pipe thickness ratio ranging from 0.20 to 0.57 and fluid (gauge) pressure in the range of 0 to 10 atmospheres are examined. The rotational spring stiffness is obtained by an inverse vibration analysis and deflection method. The details of the two methods are given. The results by the two methods are presented graphically and show good agreement. Crack locations are also determined by the inverse analysis. The maximum absolute error in the location is 13.80%. Experimentally determined variation of rotational spring stiffness with ratio of crack size to thickness is utilized to predict the crack sizes. The maximum absolute errors in prediction of crack size are 17.24% and 16.90% for aluminium and mild steel pipes respectively.

Key Words
detection of crack; out-of-plane transverse vibration; L-shaped pipe filled with fluid; transfer matrix method; rotational spring.

Address
Mechanical Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

Abstract
The novel form of composite walling system consists of two skins of profiled steel sheeting with an in-fill of concrete. The behaviour of such walling under in-plane shear is important in order to utilise this system as shear elements in a steel framed building. Steel sheet-concrete interface governs composite action, overall behaviour and failure modes of such walls. This paper describes the finite element (FE) modelling of the shear behaviour of walls with particular emphasis on the simulation of steel-concrete interface. The modelling of complex non-linear steel-concrete interaction in composite walls is conducted by using different FE models. Four FE models are developed and characterized by their approaches to simulate steel-concrete interface behaviour allowing either full or partial composite action. Non-linear interface or joint elements are introduced between steel and concrete to simulate partial composite action that allows steel-concrete in-plane slip or out of plane separation. The properties of such interface/joint elements are optimised through extensive parametric FE analysis using experimental results to achieve reliable and accurate simulation of actual steel-concrete interaction in a wall. The performance of developed FE models is validated through small-scale model tests. FE models are found to simulate strength, stiffness and strain characteristics reasonably well. The performance of a model with joint elements connecting steel and concrete layers is found better than full composite (without interface or joint elements) and other models with interface elements. The proposed FE model can be used to simulate the shear behaviour of composite walls in practical situation.

Key Words
profiled composite wall; shear strength; finite element modeling; steel-concrete interface.

Address
K. M. Anwar Hossain; Department of Civil Engineering, Ryerson University, 350 Victoria Street, Toronto,
Ontario, M5B 2K3, Canada
H. D. Wright; Department of Civil Engineering, University of Strathclyde, Glasgow, UK

Abstract
In engineering practice, tubular connections are usually assumed pinned or rigid. Recent research showed that tubular joints may exhibit non-rigid behavior under axial or bending loads. This paper is concerned with establishing a new classification for tubular joints and investigating the effect of joint rigidity on the global behavior of CHS (Circular Hollow Section) lattice girders. Parametric formulae for predicting tubular joint rigidities are proposed, which are based on the finite element analyses through systematic variation of the main geometric parameters. Comparison with test results proves the reliability of these formulae. By considering the deformation patterns of respective parts of Vierendeel lattice girders, the boundary between rigid and semirigid tubular connections is built in terms of joint bending rigidity. In order to include characteristics of joint rigidity in the global structural analysis, a type of semirigid element which can effectively reflect the interaction of two braces in K joints is introduced and validated. The numerical example of a Warren lattice girder with different joint models shows the great effect of tubular joint rigidities on the internal forces, deformation and secondary stresses.

Key Words
non-rigid behavior; tubular joint rigidity; finite element analysis; tubular joints classification; semirigid element; CHS lattice girder.

Address
College of Civil Engineering, Tongji University,
Shanghai 200092, China

Abstract
The response of a plate-column system having five-degree-of-freedom supported by an elastic foundation and subjected to static lateral load, harmonic ground motion and earthquake motion is studied. Two Winkler foundation models are assumed: a conventional model which supports compression and tension and a tensionless model which supports compression only. The governing equations of the problem are obtained, solved numerically and the results are presented in figures to demonstrate the behavior of the system for various values of the system parameters comparatively for the conventional and the tensionless Winkler foundation models.

Key Words
rectangular plate; plate-column system; tensionless foundation; Winkler foundation; static and dynamic loads.

Address
Department of Structural and Earthquake Engineering, Faculty of Civil Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey

Abstract
Due to the complexity of mathematical expressions, the literature concerning the free vibration analysis of plates carrying multiple three-degree-of-freedom (dof) spring-mass systems is rare. In this paper, the three degrees of freedom (dof?) for a spring-mass system refer to the translational motion of its lumped mass in the vertical direction and the two pitching motions of its lumped mass about the two horizontal ( and ) axes. The basic concept of this paper is to replace each three-dof spring-mass system by a set of equivalent springs, so that the free vibration characteristics of a rectangular plate carrying any number of three-dof spring-mass systems can be obtained from those of the same plate supported by the same number of sets of equivalent springs. Since the three dof? of the lumped mass for each three-dof spring-mass system are eliminated to yield a set of equivalent springs, the total dof of the entire vibrating system is not affected by the total number of the spring-mass systems attached to the rectangular plate. However, this is not true in the conventional finite element method (FEM), where the total dof of the entire vibrating system increases three if one more three-dof spring-mass system is attached to the rectangular plate. Hence, the computer storage memory required by using the presented equivalent spring method (ESM) is less than that required by the conventional FEM, and the more the total number of the three-dof spring-mass systems attached to the plate, the more the advantage of the ESM. In addition, since manufacturing a spring with the specified stiffness is much easier than making a three-dof spring-mass system with the specified spring constants and mass magnitude, the presented theory of replacing a three-dof spring-mass system by a set of equivalent springs will be also significant from this viewpoint.

Key Words
equivalent spring method; finite element method; rectangular plate; three-dof spring-mass system; free vibration.

Address
Department of Marine Engineering, National Kaohsiung Marine University, No. 142, Hai-Chuan Road, Nan-Tzu, Kaohsiung 811, Taiwan, Republic of China

Abstract
This paper presents a theoretical model for the behavior of partially confined axi-symmetric reinforced concrete members subjected to axial load. The analysis uses the theories of elasticity and plasticity to cover the full range of the concrete behavior. Analysis of the elastic range of the problem involves boundary conditions that are defined along a relatively simple geometry. However, extending the analysis into the plastic range involves difficulties that arise from the irregular geometry of the boundary between the plastic zone and the elastic zone, a boundary which is also changing as the axial load increases. The solution is derived by replacing the discrete steel ties with an equivalent tube of thickness teq and by analyzing the concrete cylinder, which is uniformly confined by the equivalent tube. The equivalency criterion initiates from a theoretical analysis of the problem in its elastic range where further finite element analysis shows that this criterion is valid also for the plastic range of the cylinder material. According to the proposed model, the efficiency of the lateral reinforcement can be evaluated by the equivalent thickness teq. Comparison with published test results of confined reinforced concrete stress-strain curves shows good agreement between the test and the analytical results.

Key Words
confined concrete; steel ties; plasticity.

Address
R. Eid; Department of Civil Engineering, University of Sherbrooke, Sherbrooke, Quebec, Canada J1J 2R1
A. N. Dancygier; National Building Research Institute, Department of Structural Engineering and Construction Management, Faculty of Civil and Environmental Engineering, Technion-Israel Institute of Technology,
Technion City, Haifa 32000, Israel


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