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Volume 12, Number 1, July 2001

A reliable and accurate method has been developed to predict the flexural deformation
response of structural concrete members subject to service load. The method that has been developed
relates the extent of concrete cracking, measured as a function of the magnitude of applied moment in a
member, to the reduction in the effective moment of inertia of cracked reinforced concrete members under
service load conditions. The ratio of the area of the moment diagram where the moment exceeds the
cracking moment, to the total area of the moment diagram for any loading, provides the basis for the
calculation of the effective moment of inertia. This ratio also represents mathematically a probability of
crack occurrence. Verification of this method for the determination of the effective moment of inertia has
been achieved from an experimental test program, and has included beam tests with different loading
configurations, and shear wall tests subjected to a range of vertical and lateral load levels. Further
verification of this method has been made with reference to the experimental investigation of other
recently published work.

Key Words
probability; flexural members; deflection; curvature; stiffness; serviceability prediction; moment of inertia; cracking; reinforced concrete.

Feng Ning, Neil C. Mickleborough and Chun-Man Chan, Department of Civil Engineering, Hong Kong University of Science & Technology, Kowloon, Hong Kong

The frictionless contact problem for a layered composite which consists of two elastic layers
having different elastic constants and heights resting on two simple supports is considered. The external
load is applied to the layered composite through a rigid stamp. For values of the resultant compressive
force P acting on the stamp vertically which are less than a critical value Pcr and for small flexibility of
the layered composite, the continuous contact along the layer - the layer and the stamp - the layered
composite is maintained. However, if the flexibility of the layered composite increases and if tensile
tractions are not allowed on the interface, for P > Pcr, a separation may be occurred between the stamp
and the layered composite or two elastic layers interface along a certain finite region. The problem is
formulated and solved for both cases by using Theory of Elasticity and Integral Transform Technique.
Numerical results for Pcr, separation initiation distance, contact stresses, distances determining the
separation area, and the vertical displacement in the separation zone between two elastic layers are given.

Key Words
continuous contact; discontinuous contact; separation; integral equation; elastic layer; rigid stamp; theory of elasticity; fourier transform.

Ahmet Birinci and RagIp Erdol, Civil Engineering Department, Karadeniz Technical University, 61080, Trabzon, Turkey

A numerical methodology is presented in this paper for the geometrically non-linear analysis
of slender uni-dimensional structural elements under unilateral contact constraints. The finite element method
together with an updated Lagrangian formulation is used to study the structural system. The unilateral
constraints are imposed by tensionless supports or foundations. At each load step, in order to obtain the
contact regions, the equilibrium equations are linearized and the contact problem is treated directly as a
minimisation problem with inequality constraints, resulting in a linear complementarity problem (LCP).
After the resulting LCP is solved by Lemke

Key Words
unilateral constraints; incremental-iterative strategies; geometric non-linearity; updated Lagrangian formulation; linear complementary problem.

Ricardo Azoubel da Mota Silveira, Civil Engineering Department, Federal University of Ouro Preto (UFOP) Morro do Cruzeiro-Campus Universitario, 35400-000 Ouro Preto, MG, Brazil
Paulo Batista Goncalves, Civil Engineering Department, Catholic University, PUC-Rio Rua Marques de Sao Vicente, 225 - Gavea, 22453-900 Rio de Janeiro, RJ, Brazil

Whereas the potential of static inelastic analysis methods is recognised in earthquake design
and assessment, especially in contrast with elastic analysis under scaled forces, they have inherent
shortcomings. In this paper, critical issues in the application of inelastic static (pushover) analysis are
discussed and their effect on the obtained results appraised. Areas of possible developments that would
render the method more applicable to the prediction of dynamic response are explored. New developments
towards a fully adaptive pushover method accounting for spread of inelasticity, geometric nonlinearity, full
multi-modal, spectral amplification and period elongation, within a framework of fibre modelling of
materials, are discussed and preliminary results are given. These developments lead to static analysis
results that are closer than ever to inelastic time-history analysis. It is concluded that there is great scope
for improvements of this simple and powerful technique that would increase confidence in its employment
as the primary tool for seismic analysis in practice.

Key Words
seismic analysis; pushover; inelastic response.

A.S. Elnashai, Engineering Seismology and Earthquake Engineering Section
Civil and Environmental Engineering Department, Imperial College, London SW7 2BU, UK

The objective of this paper is to develop a simplified method that could predict the strength
of concrete filled steel tube (CFT) columns applicable to high strength material under combined axial
compression and flexure. The simplified method for determining the strength of CFT columns is based on
the interaction curve of the section approached by a polygonal connection of the points. These points are
determined by using symmetrical properties of the CFT section. For each point, a simple equation is
proposed to determine the strength of the slender columns under compression and flexure. The simple
equation was adjusted with results of elasto-plastic analysis results. Validation of the simplified method is
undertaken by comparison with data from the test conducted at Kyushu University. These results confirm
the fact that the simplified method could accurately and reliably predict the strength of CFT columns
under combined axial compression and flexure.

Key Words
concrete filled steel tubular columns; simplified design formula; high strength material.

Jinan Chung, Department of Architecture, Fukuoka University, 8-19-1 Nanakuma Jonanku, Fukuoka, Japan
Chiaki Matsui

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform
beams is proposed. It is shown that the governing differential equations for several stability, free
vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate
differential equation of the second-order. There are two functions in the unified equation, unlike most
previous researches dealing with this problem, one of the functions is selected as an arbitrary expression
in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using
appropriate functional transformation, the self-conjugate equation is reduced to Bessel

Key Words
non-uniform beam; stability; vibration; dynamic.

Q.S. Li, Department of Building and Construction, City University of Hong Kong
Tat Chee Avenue, Kowloon, Hong Kong

The reliable prediction of elastic vibrations of wetted complex structures, as ships, tanks,
offshore structures, propulsion components etc. represent a theoretical and numerical demanding task due
to fluid-structure interaction. The paper presented is addressed to the vibration analysis by a combined
FE-BE-procedure based on the added mass concept utilizing a direct boundary integral formulation of the
potential fluid problem in interior and exterior domains. The discretization is realized by boundary
element collocation method using conventional as well as infinite boundary element formulation with
analytical integration scheme. Particular attention is devoted to modelling of interior problems with both
several separate or communicating fluid domains as well as thin-walled structures wetted on both sides.
To deal with this specific kind of interaction problems so-called

Key Words
fluid structure interaction; vibration analysis; coupled finite and boundary element method;

Udo Rohr and Peter Moller, Department of Mechanical Engineering, University of Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany

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