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Abstract
Ductility of open piled wharves under reversed cyclic loads has been investigated.
Experimental testing of five wharf models having a scale of about 1:4 was conducted under the
application of horizontal reversed cyclic loading. The experiments were designed to focus on the
horizontal ultimate load, ductility and failure mode of the considered wharf models. Nonlinear numerical
analyses using the finite element method were also performed on numerical models representing the
experimentally tested wharves. The results of the experimental tests showed that open piled wharves
possessed favourable ductile behaviour and that their load bearing capacity did not depreciate until a
ductility factor of 3 to 4 was reached. The numerical analysis showed that the relative rotation that took
place at the joints between the steel piles and the R.C. beam was responsible for a considerable portion of
the total horizontal deformation of the wharves. Therefore, it was concluded that introducing the joint
stiffness in calculating the deformations of open piled wharves was important to achieve reasonable
accuracy.

Key Words
open piled wharf; steel pile; seismic design; ultimate stage; experimental tests; nonlinear analysis.

Address
Hiroshi Yokota, Port and Airport Research Institute, Yokosuka, Japan
Hazem M.F. El-Bakry, Structural Engineering Department, Alexandria University, Alexandria, Egypt

Abstract
In this paper, modal control with direct output feedback is formulated in a systematic manner
for easy implementation. Its application to the seismic protection of structural systems is verified by a
shaking table test, which involves a full-scale building model and an active bracing system as the control
device. Two modal control cases, namely, one full-state feedback and one direct output feedback control
were tested and compared. The experimental result shows that in mitigating the seismic response of
building structures, modal control with direct output feedback can be as effective and efficient as that with
full-state feedback control. For practical concerns, the control performance of the proposed method in the
presence of sensor noise and stiffness modeling error was also investigated. The numerical result shows
that although the control force may be increased, the maximum floor displacements of the controlled
structure are very insensitive to sensor noise and modeling error.

Key Words
active structural control; modal control; direct output feedback; seismic protection; active bracing system; shaking table test.

Address
Lyan-Ywan Lu, Department of Construction Engineering, National Kaohsiung First University of Science and Technology, University Road, Yenchao, Kaohsiung 824, Taiwan

Abstract
Fiber reinforced cementitious composites are nowadays widely applied in civil engineering.
The postcracking performance of this material depends on the interaction between a steel fiber, which is
obliquely across a crack, and its surrounding matrix. While the partly debonded steel fiber is subjected to
pulling out from the matrix and simultaneously subjected to transverse force, it may be modelled as a
Bernoulli-Euler beam partly supported on an elastic foundation with non-linearly varying modulus. The
fiber bridging the crack may be cut into two parts to simplify the problem (Leung and Li 1992). To
obtain the transverse displacement at the cut end of the fiber (Fig. 1), it is convenient to directly solve the
corresponding differential equation. At the first glance, it is a classical beam on foundation problem.
However, the differential equation is not analytically solvable due to the non-linear distribution of the
foundation stiffness. Moreover, since the second order deformation effect is included, the boundary
conditions become complex and hence conventional numerical tools such as the spline or difference
methods may not be sufficient. In this study, moment equilibrium is the basis for formulation of the
fundamental differential equation for the beam (Timoshenko 1956). For the cantilever part of the beam,
direct integration is performed. For the non-linearly supported part, a transformation is carried out to
reduce the higher order differential equation into one order simultaneous equations. The Runge-Kutta
technique is employed for the solution within the boundary domain. Finally, multi-dimensional
optimization approaches are carefully tested and applied to find the boundary values that are of interest.
The numerical solution procedure is demonstrated to be stable and convergent.

Key Words
beam on elastic foundation; non-linear modulus; boundary conditions; cantilever; higher order differential equation; Runge-Kutta technique; optimization approach; downhill simplex method; genetic algorithms.

Address
Xiao Dong Hu, Robert Day and Peter Dux, Department of Civil Engineering, The University of Queensland, St. Lucia, QLD 4072, Brisbane, Australia

Abstract
A new method for solving the uncertain eigenvalue problems of the structures with interval
parameters, interval finite element method based on the element, is presented in this paper. The
calculations are done on the element basis, hence, the efforts are greatly reduced. In order to illustrate the
accuracy of the method, a continuous beam system is given, the results obtained by it are compared with
those obtained by Chen and Qiu (1994); in order to demonstrate that the proposed method provides safe
bounds for the eigenfrequencies, an undamping spring-mass system, in which the exact interval bounds
are known, is given, the results obtained by it are compared with those obtained by Qiu et al. (1999),
where the exact interval bounds are given. The numerical results show that the proposed method is
effective for estimating the eigenvalue bounds of structures with interval parameters.

Key Words
interval parameters; interval eigenvalue analysis; interval finite element method.

Address
Xiaowei Yang, Department of Applied Mathematics, South China University of Technology, Guangzhou 510640, China
Suhuan Chen and Huadong Lian, Department of Mechanics, Jilin University, Changchun 130025, China

Abstract
In this paper, a general method for the automatic search for Strut-and-Tie (S&T) models
representative of possible resistant mechanisms in reinforced concrete elements is proposed. The
representativeness criterion here adopted is inspired to the principle of minimum strain energy and
requires the consistency of the model with a reference stress field. In particular, a highly indeterminate
pin-jointed framework of a given layout is generated within the assigned geometry of the concrete
element and an optimum truss is found by the minimisation of a suitable objective function. Such a
function allows us to search the optimum truss according to a reference stress field deduced through a
F.E.A. and assumed as representative of the given continuum. The theoretical principles and the
mathematical formulation of the method are firstly explained; the search for a S&T model suitable for the
design of a deep beam shows the method capability in handling the reference stress path. Finally, since
the analysis may consider the structure as linear-elastic or cracked and non-linear in both the component
materials, it is shown how the proposed procedure allows us to verify the possibilities of activation of the
design model, oriented to the serviceability condition and deduced in the linear elastic field, by following
the evolution of the resistant mechanisms in the cracked non-linear field up to the structural failure.

Key Words
Strut-and-Tie models; R.C. analysis and design; structural optimisation.

Address
Fabio Biondini, Department of Structural Engineering, Technical University of Milan, Piazza L. da Vinci 32, 20133 Milan, Italy
Franco Bontempi, Department of Structural and Geotechnical Engineering, University of Rome \"La Sapienza\", Via Eudossiana 18, 00184 Rome, Italy
Pier Giorgio Malerba, Department of Structural Engineering, Technical University of Milan, Piazza L. da Vinci 32, 20133 Milan, Italy

Abstract
This paper discusses the elastic stability of unbraced frames under non-proportional loading
based on the concept of storey-based buckling. Unlike the case of proportional loading, in which the load
pattern is predefined, load patterns for non-proportional loading are unknown, and there may be various
load patterns that will correspond to different critical buckling loads of the frame. The problem of
determining elastic critical loads of unbraced frames under non-proportional loading is expressed as the
minimization and maximization problem with subject to stability constraints and is solved by a linear
programming method. The minimum and maximum loads represent the lower and upper bounds of critical
loads for unbraced frames and provide realistic estimation of stability capacities of the frame under
extreme load cases. The proposed approach of evaluating the stability of unbraced frames under non-proportional
loading has taken into account the variability of magnitudes and patterns of loads, therefore,
it is recommended for the design practice.

Key Words
non-proportional loading; frame stability; storey-based buckling; linear programming; critical load; unbraced frame; lean-on column.

Address
L. Xu, Y. Liu and J. Chen, Department of Civil Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Abstract
An improved method has been developed for the computation of the section forces and
stiffness in nonlinear finite element analysis of RC plane frames. The need for a new approach arises
because the conventional technique may have a questionable level of efficiency if a large number of
layers is specified and a questionable level of accuracy if a smaller number is used. The proposed
technique is based on automatically dividing the section into zones of similar state of stress and tangent
modulus and then numerically integrating within each zone to evaluate the sectional stiffness parameters
and forces. In the new system, the size, number and location of the layers vary with the state of the
strains in the cross section. The proposed method shows a significant improvement in time requirement
and accuracy in comparison with the conventional layered approach. The computer program based on the
new technique has been used successfully to predict the experimental load-deflection response of a RC
frame and good agreement with test and other numerical results have been obtained.

Key Words
computation; computer analysis; concrete structures; finite element analysis; layered systems; nonlinear analysis; nonlinear response; efficiency.

Address
Ahmed B. Shuraim, Civil Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Abstract
The objective of this study is to investigate the stability behavior of steel cable-stayed
bridges by comparing the buckling loads obtained by means of finite element methods with eigen-solver.
In recent days, cable-stayed bridges dramatically attract engineers

Key Words
stability analysis; cable-stayed bridges; steel and bridge.

Address
Chia-Chih Tang, Hung-Shan Shu and Yang-Cheng Wang, Department of Civil Engineering, Chinese Military Academy, Taiwan, 1 Hwang-Poo Road, Feng-Shan, 83000, Taiwan, ROC

Abstract
This paper is concerned with a study on thermo-elastoplastic characteristics of functionally
graded composite. Compared to the classical layered composites, it shows a wide range of thermo-elastoplastic
characteristics according to the choice of two major parameters, the thickness-wise volume
fraction of constituents and the relative thickness ratio of the graded layer. Therefore, by selecting an
appropriate combination of the two parameters, one is expected to design the most suitable heat-resisting
composite for a given thermal circumstance. Here, we address the parametric investigation on its characteristics together with theoretical study on thermo-elastoplasticity and numerical techniques for its finite
element approximations. Through the numerical experiments, we examine the influence of two parameters
on the thermo-elastoplastic characteristics.

Key Words
functionally graded material (FGM); graded layer; volume fraction; relative thickness ratio; material properties; stress concentration; thermo-elastoplastic characteristics.

Address
Jin-Rae Cho and Dae-Yul Ha, School of Mechanical Engineering, Pusan National University, Pusan 609-735, Korea

Abstract
A frequency domain response analysis is presented for building frames passively controlled
by viscoelastic dampers, under harmonic ground excitation. Three different models are used to represent
the linear dynamic force-deformation characteristics of viscoelastic dampers namely, Kelvin model, Linear
hysteretic model and Maxwell model. The frequency domain solution is obtained by (i) an iterative
pseudo-force method, which uses undamped mode shapes and frequencies of the system, (ii) an
approximate modal strain energy method, which uses an equivalent modal damping of the system in each
mode of vibration, and (iii) an exact method which uses complex frequency response function of the
system. The responses obtained by three different methods are compared for different combinations of
viscoelastic dampers giving rise to both classically and non-classically damped cases. In addition, the
effect of the modelling of viscoelastic dampers on the response is investigated for a certain frequency
range of interest. The results of the study are useful in appropriate modelling of viscoelastic dampers and
in understanding the implication of using modal analysis procedure for building frames which are
passively controlled by viscoelastic dampers against base excitation.

Key Words
viscoelastic dampers; base excitation; storage and loss moduli; pseudo-force; modal strain energy.

Address
A.K. Shukla and T.K. Datta, Civil Engineering Department, Indian Institute of Technology, New Delhi 110 016, India

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