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Volume 13, Number 3, March 2002

The effect of shear coupled with axial force variation on the inelastic seismic behaviour of
reinforced concrete bridge piers is investigated in this paper. For this purpose, a hysteretic axial-shear
interaction model was developed and implemented in a nonlinear finite element analysis program. Thus,
flexure-shear-axial interaction is simulated under variable amplitude reversed actions. Comparative studies
for shear-dominated reinforced concrete columns indicated that a conventional FE model based on flexure-axial
interaction only gave wholly inadequate results and was therefore incapable of predicting the
behaviour of such members. Analysis of a reinforced concrete bridge damaged during the Northridge
(California 1994) earthquake demonstrated the importance of shear modelling. The contribution of shear
deformation to total displacement was considerable, leading to increased ductility demand. Moreover, the
effect of shear with axial force variation can significantly affect strength, stiffness and energy dissipation
capacity of reinforced concrete members. It is concluded that flexure-shear-axial interaction should be
taken into account in assessing the behaviour of reinforced concrete bridge columns, especially in the
presence of high vertical ground motion.

Key Words
reinforced concrete; bridges; columns; hysteretic response; shear deformation; axial force variation

Do Hyung Lee, Department of Civil and Geotechnical Engineering, Paichai University, 439-6 Doma 2 dong, Seo-ku, Daejeon, Korea
Amr S. Elnashai, Structural Engineering, 2129e CEE Department, University of Illinois at Urbana-Champaign, 205 North Mathews Avenue, Urbana, IL 61801-2397, USA

A novel, 6-node, two-dimensional mixed finite element (FE) model has been developed to
analyze laminated composite beams by using the minimum potential energy principle. The model has
been formulated by considering four degrees of freedom (two displacement components u, w and two
transverse stress components sz, txz) per node. The transverse stress components have been invoked as
nodal degrees of freedom by using the fundamental elasticity equations. Thus, the present mixed finite
element model not only ensures the continuity of transverse stress and displacement fields through the
thickness of the laminated beams but also maintains the fundamental elasticity relationship between the
components of stress, strain and displacement fields throughout the elastic continuum. This is an
important feature of the present formulation, which has not been observed in various mixed formulations
available in the literature. Results obtained from the model have been shown to be in excellent agreement
with the elasticity solutions for thin as well as thick laminated composite beams. A few results for a
cross-ply beam under fixed support conditions are also presented.

Key Words
mixed finite element; minimum potential energy principle; laminated composite beam.

Y.M. Desai and G.S. Ramtekkar, Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India

In this study, free vibration analysis of Reissner plates on Pasternak foundation is carried out
by mixed finite element method based on the Gateaux differential. New boundary conditions are
established for plates on Pasternak foundation. This method is developed and applied to numerous
problems by Akoz and his co-workers. In dynamic analysis, the problem reduces to the solution of a
standard eigenvalue problem and the mixed element is based upon a consistent mass matrix formulation.
The element has four nodes and bending and torsional moments, transverse shear forces, rotations and
displacements are the basic unknowns. The element performance is assessed by comparison with
numerical examples known from literature. Validity limits of Kirchhoff plate theory is tested by dynamic
analysis. Shear locking effects are tested as far as h/2a =10 -6 and it is observed that REC32 is free from
shear locking.

Key Words
Reissner plate, free vibration, Pasternak, mixed-finite element.

Nihal Eratl and A. Yalcin Akoz, Faculty of Civil Engineering, Istanbul Technical University, 80626 Maslak-Istanbul, Turkey

In this paper, a new method to solve the dynamic response problem for structures with
interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an
optimum scheme is adopted when there are many interval structural parameters. With the interval
algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are
developed. Based on the matrix perturbation theory and interval extension of function, the upper and
lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval
operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to
illustrate the validity of the present method.

Key Words
interval extension of function; interval characters matrices; matrix perturbation theory; interval of dynamic response.

Su Huan Chen and Hua Dong Lian, Department of Mechanics, Jilin University, Changchun 130025, P.R. China
Xiao Wei Yang, Department of Applied Mathematics, South China University of Technology, Guangzhou 510640, P.R. China

Based on the orthotropic hypoelasticity formulation, a triaxial constitutive model of concrete
is proposed. To account for increasing ductility in high confinement of concrete, the ductility enhancement
is considered using so called the strain enhancement factor. It is also developed a three-dimensional finite
element model for reinforced concrete structural members based on the proposed constitutive law of
concrete with the smeared crack approach. The concrete confinement effects due to the beam-column joint
are investigated through numerical examples for simple beam and structural beam member. Concrete at
compression fibers in the vicinity of beam-column joint behaves dominant not only by the uniaxial
compressive state but also by the biaxial and triaxial compressive states. For the reason of the severe
confinement of concrete in the beam-column joint, the flexural critical cross-section is observed at a small
distance away from the beam-column joint. These observations should be utilized for the economic design
when the concrete structural members are subjected to high confinement due to the influence of beam-column

Key Words
compressive strength of concrete; hypoelastic model; finite element analysis; concrete confinement due to beam-column joint.

Chang-Geun Cho, Research Institute for Disaster Prevention, Kyungpook National University, Sankyuk-Dong 1370, Puk-Ku, Taegu, Korea
Hisato Hotta, Department of Architecture and Building Engineering, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-Ku, Tokyo, Japan

In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduli
and density varying in the thickness direction, subject to a uniform external pressure which is a power function
of time, has been studied. After giving the fundamental relations, the dynamic stability and compatibility
equations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external pressure, have
been derived. Applying Galerkin

Key Words
dynamic stability; nonhomogeneous; orthotropic; truncated; conical shell; external pressure; Galerkin

A.H. Sofiyev, Ondokuz Mayis University, Civil Engineering Department, 55139, Samsun, Turkey
O. Aksogan, Cukurova University, Civil Engineering Department, 01330, Adana, Turkey

Three noded plate and shell finite element and 3D beam element in conjunction with
Lanczos method are used for studying the effect of boat tail angle on the free vibration characteristics of
a typical payload fairing for three different cylinder diameters with height to diameter ratio 1.5.
Configurations without boat tail structural member are also studied. One half of the one side fairing
structure is considered for the analysis and symmetric boundary conditions are used.

Key Words
finite element method; Lanczos method; payload fairing.

V. Ramamurti, Machine Dynamics Laboratory, Indian Institute of Technology, Madras 600036, India
S. Rajarajan, Launch Vehicle Design Group, Vikram Sarabhai Space Centre, Trivandrum 695022, India
G. Venkateswara Rao, Structural Engineering Group, Vikram Sarabhai Space Centre, Trivandrum 695022, India

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