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Volume 12, Number 6, December 2001

A two-level displacement-based design procedure is developed. To obtain the displacement
demands, elastic spectra for occasional earthquakes and inelastic spectra for rare earthquakes are used.
Minimum global stiffness and strength to be supplied to the structure are based on specified maximum
permissible drift limits and on the condition that the structure responds within the elastic range for
occasional earthquakes. The performance of the structure may be assessed by an inelastic push-over
analysis to the required displacement and the evaluation of damage indices. The approach is applied to the
design of a five-story reinforced concrete coupled wall structure located in the most hazardous seismic
region of Argentina. The inelastic dynamic response of the structure subjected to real and artificially
generated acceleration time histories is also analyzed. Finally, advantages and limitations of the proposed
procedure from the conceptual point of view and practical application are discussed.

Key Words
performance based seismic design; earthquake resistant structures; reinforced concrete buildings; inelastic seismic analysis; damage evaluation.

Marcelo Rubinstein and Oscar Moller, Instituto de Mecanica Aplicada y Estructuras, Universidad Nacional de Rosario, Riobamba y Berutti, 2000 Rosario, Argentina
Alejandro Giuliano, Instituto Nacional de Prevencion Sismica, Roger Balet 47N, 5400 San Juan, Argentina

This paper studies the behaviour of a homogeneous cable in a horizontal rigid duct and
loaded by an axial compressive force. This behaviour is characterized by spatial buckling modes, named
sinusoidal and helical, due to friction and total or partial cable locking. The evaluation of critical buckling
loads involved by drilling technology has been studied by many authors. This work presents a new
formulation, taking the friction effects into account, for the transmission of the axial load during the
postbuckling process. New analytical expressions of pitches in both buckling cases are also given. A life-sized
bench is presented, which permits to study the laying of optical fiber cables by squeezing them into
an underground duct. Finally, analytical solutions are compared with experimental tests and finite element

Key Words
beam; buckling; postbuckling; boundary conditions; contact analytical; experimental; finite element results.

L. Rivierre, France Telecom, CNET Lannion-DTD/IBL, BP40, 22307 Lannion cedex, France
O. Polit, LMpX-Universite Paris X-1 Chemin, Desvallieres-92410 Ville d

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

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

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

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.

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

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.

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

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.

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

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.

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

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