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CONTENTS
Volume 22, Number 6, April20 2006
 

Abstract
The main purpose of this paper is to investigate the effect of transient stochastic analysis on nonlinear response of earth and rock-fill dams to spatially varying ground motion. The dam models are analyzed by a stochastic finite element method based on the equivalent linear method which considers the nonlinear variation of soil shear moduli and damping ratio as a function of shear strain. The spatial variability of ground motion is taken into account with the incoherence, wave-passage and site response effects. Stationary as well as transient stochastic response analyses are performed for the considered dam types. A time dependent frequency response function is used throughout the study for transient stochastic responses. It is observed that stationarity is a reasonable assumption for earth and rock-fill dams to typical durations of strong shaking.

Key Words
spatially varying ground motion; stationary response; transient response; equivalent linear method; earth-fill dam; rock-fill dam; stochastic response.

Address
Karadeniz Technical University, Department of Civil Engineering, 61080 Trabzon, Turkey

Abstract
The strength behaviors of Fiber Reinforced Plastics (FRP) Composites can be greatly influenced by the properties of constitutive materials, the laminate structures, and load conditions etc, accompanied by many uncertainty factors. So the reliability study on FRP is an important subject of research. Many achievements have been made in reliability studies based on the probability theory, but little has been done on the roles played by fuzzy variables. In this paper, a fuzzy reliability model for FRP laminates is established first, in which the loads are considered as random variables and the strengths as fuzzy variables. Then a numerical model is developed to assess the fuzzy reliability. The Monte Carlo simulation method is utilized to compute the reliability of laminas under the maximum stress criterion. In the second part of this paper, a generalized fuzzy reliability model (GFRM) is proposed. By virtue of the fact that there may exist a series of states between the failure state and the function state, a fuzzy assumption for the structure state together with the probabilistic assumption for strength parameters is adopted to construct the GFRM of composite materials. By defining a generalized limit state function, the problem is converted to the conventional reliability formula that enables the first-order reliability method (FORM) applicable in calculating the reliability index. Several examples are worked out to show the validity of the models and the efficiency of the methods proposed in this paper. The parameter sensitivity analysis shows that some of the mean values of the strength parameters have great influence on the laminated composites?reliability. The differences resulting from the application of different failure criteria and different fuzzy assumptions are also discussed. It is concluded that the GFRM is feasible to use, and can provide an effective and synthetic method to evaluate the reliability of a system with different types of uncertainty factors.

Key Words
laminated composites; fuzzy reliability; Monte Carlo simulation; generalized limit state function.

Address
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract
The effective length factor is a familiar concept for practicing engineers and has long been an approach for column stability evaluations. Neglecting the effects of axial force in the restraining members, in the case of sway prevented frames, is one of the simplifying assumptions which the Alignment Charts, the conventional nomographs for K-Factor determination, are based on. A survey on the problem reveals that the K-Factor of the columns may be significantly affected when the differences in axial forces are taken into account. In this paper a new iterative approach, with high convergence rate, based on the general principles of structural mechanics is developed and the patterns for detection of the critical member are presented and discussed in details. Such facilities are not available in the previously presented methods. A constructive methodology is outlined and the usefulness of the proposed algorithm is illustrated by numerical examples.

Key Words
effective length factor; K-factor; frame stability; column buckling; braced frame.

Address
M. R. Mahini; Civil Engineering Group, Persian Gulf University, Boushehr, Iran
H. Seyyedian; Civil Engineering Department, Shiraz University, Shiraz, Iran

Abstract
In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ? etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

Key Words
multiple-step beam; lumped mass; rotary inertia; exact natural frequency; mode shape; integration constants.

Address
Hsien-Yuan Lin; Dept. of Mechanical and Electro
Mechanical Engineering, Nat. Sun Yat-Sen University,
70, Lien-hai Road, Kaohsiung 804, Taiwan, ROC
Ying-Chien Tsai; Dept. of Mechanical and Electro-Mechanical Engineering, Nat. Sun Yat-Sen University,
70, Lien-hai Road, Kaohsiung 804, Taiwan, ROC
(Dept. of Mechanical Engineering, Cheng Shiu Univ.,
Kaohsiung 833, Taiwan, ROC)

Abstract
An analytical method for the free vibration of two circular plates coupled with an inviscid and compressible fluid is developed by the Rayleigh-Ritz method. The fluid is bounded by a rigid cylindrical vessel and two circular plates with an unequal thickness and diameter. It was found that the theoretical results could predict well the fluid-coupled natural frequencies with an excellent accuracy when compared with the finite element analysis results. As the fluid thickness increases or the plate thickness difference increases, an abrupt curve veering in the natural frequency loci of the neighboring modes and drastic changes in the corresponding mode shapes are observed. The mode localization frequently appears in the higher modes and in the wide gap between the plates because of a decrease in the fluid coupling owing to the fluid dispersion effect.

Key Words
hydroelastic vibration; fluid-structure interaction; circular plates; mode localization; veering of natural frequency loci; Rayleigh-Ritz method.

Address
Mechanical Engineering Division, Korea Atomic Energy Research Institute, P. O. Box 105, Yuseong, Daejeon 305-600, Republic of Korea

Abstract
A general theory which describes the elastic response of a curved anisotropic plate subjected to stretching and bending will be developed by considering the nonlinear effect that reflecting the non-flat geometry of the structure. By applying a newly derived 6 ?6 matrix constitutive relation between force resultants, moment resultants, mid-plane strains and deformed curvatures, the governing differential equations for a curved anisotropic plate is developed in the usual manner, namely, by consideration of the constitutive relation and equilibrium equations. Solutions are obtained for simply-supported boundary conditions and compared to corresponding solutions that neglecting the nonlinear effect in the analysis. The comparisons indicate that the nonlinear terms in the equations that caused by the curvature of the structure is crucial for the curved plate analysis. Under certain curved plate geometries the unreasonable results will be induced by neglecting the nonlinear effect in the analysis.

Key Words
curved anisotropic plate; nonlinear; constitutive relation.

Address
Department of Mechanical Engineering, Chinese Culture University, No. 55, Hua-Kang Rd., Taipei, Taiwan

Abstract
The enlargement of interest in base isolators as an earthquake-proof design strategy has dramatically accelerated experimental studies of elastomeric bearings worldwide. In this paper, a new base isolator concept that is a hybrid system of rubber bearings is proposed. Uniaxial, biaxial, and triaxial shaking table tests are also performed to study the seismic behavior of a 0.4-scale three-story isolated steel structure in the National Center for Research on Earthquake Engineering in Taiwan. Experimental results demonstrate that structures with a hybrid system of rubber bearings composed of stirruped rubber bearings and laminated rubber bearings can actually decrease the seismic responses of the superstructure. It has been proved through the shaking table tests that the proposed hybrid system of rubber bearings is a very promising tool to enhance the seismic resistance of structures. Moreover, it is demonstrated that the proposed analytical model in this paper can predict the mechanical behavior of the hybrid system of rubber bearings and seismic responses of the base-isolated structures.

Key Words
rubber bearing; base isolation; seismic engineering; hybrid system.

Address
Bo-Jen Chen; R & D Department, Earthquake Proof Systems, Inc., Taichung, Taiwan, R.O.C.
C. S. Tsai; Department of Civil Engineering, Feng Chia University, Taichung, Taiwan, R.O.C.
L. L. Chung; National Center for Research on Earthquake Engineering, Taipei, Taiwan, R.O.C.
Tsu-Cheng Chiang; Graduate Institute of Civil and Hydraulic Engineering, Feng Chia University, Taichung, Taiwan, R.O.C.

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