Techno Press


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CONTENTS
Volume 19, Number 4, March10 2005
 

Abstract
Reinforced concrete deep beams have useful applications in tall buildings and foundations. Over the past two decades, numerous design models for deep beams were suggested. However even the latest design manuals still offer little insight into the design of deep beams in particular when complexities exist in the beams like web openings. A method commonly suggested for the design of deep beams with openings is the strut-and-tie model which is primarily used to represent the actual load transfer mechanism in a structural concrete member under ultimate load. In the present study, the development of the strut-and-tie model is transformed to the topology optimization problem of continuum structures. During the optimization process, both the stress and displacement constraints are satisfied and the performance of progressive topologies is evaluated. The influences on the strut-and-tie model in relation to different size, location and number of openings, as well as different loading and support conditions in deep beams are examined in some detail. In all, eleven deep beams with web openings are optimized and compared in nine groups. The optimal strut-and-tie models achieved are also compared with published experimental crack patterns. Numerical results have shown to confirm the experimental observations and to efficiently represent the load transfer mechanism in concrete deep beams with openings under ultimate load.

Key Words
concrete deep beams; strut-and-tie model; web openings; support conditions; topology optimization; stress and displacement constraints.

Address
School of Engineering, Griffith University Gold Coast Campus, PMB 50 Gold Coast Mail Centre,
Queensland 9726, Australia

Abstract
Base isolation technologies have been proven to be very efficient in protecting structures from seismic hazards during experimental and theoretical studies. In recent years, there have been more and more engineering applications using base isolators to upgrade the seismic resistibility of structures. Optimum design of the base isolator can lessen the undesirable seismic hazard with the most efficiency. Hence, tracing the nonlinear behavior of the base isolator with good accuracy is important in the engineering profession. In order to predict the nonlinear behavior of base isolated structures precisely, hundreds even thousands of degrees-of-freedom and iterative algorithm are required for nonlinear time history analysis. In view of this, a simple and feasible exact formulation without any iteration has been proposed in this study to calculate the seismic responses of structures with base isolators. Comparison between the experimental results from shaking table tests conducted at National Center for Research on Earthquake Engineering in Taiwan and the analytical results show that the proposed method can accurately simulate the seismic behavior of base isolated structures with elastomeric bearings. Furthermore, it is also shown that the proposed method can predict the nonlinear behavior of the VCFPS isolated structure with accuracy as compared to that from the nonlinear finite element program. Therefore, the proposed concept can be used as a simple and practical tool for engineering professions for designing the elastomeric bearing as well as sliding bearing.

Key Words
exact solution; rubber bearing; friction pendulum system; base isolation; structural control; seismic engineering.

Address
C. S. Tsai
Department of Civil Engineering, Feng Chia University, Taichung, Taiwan 407, R.O.C.

Tsu-Cheng Chiang
Graduate Institute of Civil and Hydraulic Engineering, Feng Chia University, Taichung, Taiwan 407, R.O.C.

Bo-Jen Chen
R&D Department, Earthquake Proof System, Inc, Taichung, Taiwan 404, R.O.C.

Kuei-Chi Chen
Graduate Institute of Civil and Hydraulic Engineering, Feng Chia University, Taichung, Taiwan 407, R.O.C.

Abstract
The influence of cracks on the elastic deflection and ultimate bearing capacity of eccentric thin-walled columns with both ends pinned was studied in this paper. First, a method was developed and applied to determine the elastic deflection of the eccentric thin-walled columns containing some model-I cracks. A trigonometric series solution of the elastic deflection equation was obtained by the Rayleigh-Ritz energy method. Compared with the solution presented in Okamura (1981), this solution meets the needs of compatibility of deformation and is useful for thin-walled columns. Second, a two-criteria approach to determine the stability factor j has been suggested and its analytical formula has been derived. Finally, as an example, box columns with a center through-wall crack were analyzed and calculated. The effects of cracks on both the maximum deflection and the stability coefficient j for various crack lengths or eccentricities were illustrated and discussed. The analytical and numerical results of tests on the columns show that the deflection increment caused by the cracks increases with increased crack length or eccentricity, and the critical transition crack length from yielding failure to fracture failure xc is found to decrease with an increase of the slenderness ratio or eccentricity.

Key Words
crack; thin-walled column; elastic deflection; stability factor; eccentricity; ratio of slenderness.

Address
L. Zhou
Department of Civil Engineering, Xi

Abstract
This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

Key Words
large sag deflection; variable-arc-length beams; uniformly distributed self weight; finite-element solution; shooting method; experimental studies.

Address
Tawich Pulngern
Department of Civil Engineering, King Mongkut

Abstract
In this paper, the behavior of a crack between two half-planes of functionally graded materials subjected to arbitrary tractions is resolved using a somewhat different approach, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson

Key Words
crack; functionally graded materials; Schmidt method; the dual integral equations.

Address
Zhen-Gong Zhou, Biao Wang and Lin-Zhi Wu
P.O. Box 1247, Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P. R. China

Abstract
An analytical method is presented to solve the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere subjected to thermal shock and electric excitation. Exact expressions for the transient responses of displacements, stresses, electric displacement and electric potentials in the piezoelectric hollow sphere are obtained by means of Hankel transform, Laplace transform, and inverse transforms. Using Hermite non-linear interpolation method solves Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between thermo-elastic field and thermo-electric field. Thus, an analytical solution for the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere is obtained. Finally, some numerical results are carried out, and may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

Key Words
thermo-electro-elastic; wave propagation; piezoelectric hollow sphere; electric excitation; thermal shock.

Address
H. L. Dai and X. Wang
Department of Engineering Mechanics, The School of Civil Engineering and Mechanics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

Abstract
This paper deals with a novel application of the Generalized Differential Quadrature (G.D.Q.) method to the linear elastic static analysis of isotropic rotational shells. The governing equations of equilibrium, in terms of stress resultants and couples, are those from Reissner-Mindlin shear deformation shell theory. These equations, written in terms of internal-resultants circular harmonic amplitudes, are first put into generalized displacements form, by use of the strain-displacements relationships and the constitutive equations. The resulting systems are solved by means of the G.D.Q. technique with favourable precision, leading to accurate stress patterns.

Key Words
shell of revolution; generalized differential quadrature; static analysis; numerical method.

Address
Edoardo Artioli and Erasmo Viola
D.I.S.T.A.R.T. ?Scienza delle Costruzioni, University of Bologna, Viale Risorgimento 2, Bologna, Italy


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