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CONTENTS
Volume 4, Number 3, May 1996
 

Abstract
One of the major divisions in the mathematical modelling of a tubular structure is to include the effect of the transverse shear stress and rotary inertia in vibration of members. During the past three decades, problems of vibration of tubular structures have been considered by some authors, and special attention has been devoted to the Timoshenko theory. There have been considerable efforts, also, to apply the method of spectral analysis to vibration of a structure with rectangular section beams. The purpose of this paper is to compare the results of the spectrally formulated finite element analyses for the Timoshenko theory with those derived from the conventional finite element method for a tubular structure. The spectrally formulated finite element starts at the same starting point as the conventional finite element formulation. However, it works in the frequency domain. Using a computer program, the proposed formulation has been extended to derive the dynamic response of a tubular structure under an impact load.

Key Words
spectral, finite element, vibration, tubular structure

Address
Horr AM, UNIV WOLLONGONG,DEPT CIVIL & MIN ENGN,WOLLONGONG,NSW 2522,AUSTRALIA

Abstract
An important class of problems in the field of geotechnical engineering may be analyzed with the aid of a simple integro-differential equation. Behavior of \'\'rigid\'\' piles(say concrete piles), \'\'deformable\'\' piles(say gravel piles). pile groups, pile-raft foundations, heavily reinforced earth, flow within circular silos and down drag on cylindrical structures (for example the crusher unit of a mineral processing complex) are the type of situations that can be handled by this type of equation. The equation under consideration has the form;

partial derivative w(r, z)/partial derivative + f(z)integral(0)(z)g(xi)(partial derivative(2)w(r, xi)/partial derivative r(2) + 1/r partial derivative w(r, xi)/partial derivative r)d xi + h(r, z) = 0


where w(r, z) is the vertical displacement of a soil particle expressed as a function of the polar cylindrical space coordinates (r, z) and the symbols f; g and h represent soil properties and the loading conditions. The merit of the analysis is its simplicity (both in concept and in application) and the ease with which it can be expressed in a computer code. In the present paper the analysis is applied to investigate the behavior of a single rigid pile to bedrock. The emphasis, however, is placed on equation, the numerical techique used in its evaluation and validation of the technique, hereafter called the ID technique, against a formal program, CRISP, which uses the FEM.


Key Words
soil structure, deep foundation, deformation, negative friction, numerical technique, FEM (CRISP)

Address
Poorooshasb HB, CONCORDIA UNIV,DEPT CIVIL ENGN,MONTREAL,PQ H3G 1M8,CANADA
SAGA UNIV,DEPT CIVIL ENGN,SAGA 840,JAPAN

Abstract
This paper presents a model of a layered, delaminated composite beam. The beam is modelled by beam finite elements, and the delamination is modelled by additional boundary conditions. In the present study, the laminated beam contains only one delaminated region through the thickness direction which extends to the full width of the beam. It is also assumed that the delamination is open. The influence of the delamination length and position upon changes in the bending natural frequencies of the composite laminated cantilever beam is investigated.

Key Words
natural frequencies, composite beams, delamination, finite element method

Address
Krawczuk M, POLISH ACAD SCI,INST FLUID FLOW MACHINERY,UL GEN J FISZERA 14,PL-80952 GDANSK,POLAND

Abstract
In North America, a large number of concrete old slab-on-steel girder bridges, classified noncomposite, were built without any mechanic connections. The stablizing effect due to slab/girder interface contact and friction on the steel girders was totally neglected in practice. Experimental results indicate that this effect can lead to a significant underestimation of the load-carrying capacity of these bridges.

In this paper, the two major components-concrete slab and steel girders, are treat as two deformable bodies in contact. A finite element procedure with considering the effect of friction and contact for the analysis of concrete slab-on-steel girder bridges is presented. Tile interface friction phenomenon and finite element formulation are described using an updated configuration under large deformations to account for the influence of any possible kinematic motions on the interface boundary conditions. The constitutive model for frictional contact are considered as slip work-dependent to account for the irreversible nature of friction forces and degradation of interface shear resistance, The proposed procedure is further validated by experimental bridge models.

Key Words
composite action, contact, degradation, finite element, friction

Address
Lin JJ, FORINTEK CANADA CORP,NATL WOOD PROD RES INST,VANCOUVER,BC,CANADA
UNIV LAVAL,DEPT CIVIL ENGN,QUEBEC CITY,PQ G1K 7P4,CANADA

Abstract
A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the Ist and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

Key Words
modal analysis, random eigenvalue problem, flexible connections, finite element modeling

Address
Matheu EE, VIRGINIA TECH,DEPT ENGN SCI & MECH,BLACKSBURG,VA 24061
UNIV PUERTO RICO,DEPT GEN ENGN,MAYAGUEZ,PR 00681

Abstract
The dynamic behavior of an Euler beam with multiple point constraints traversed by a moving concentrated mass, a \'\'moving-force moving-mass\'\' problem, is analyzed and compared with the corresponding simplified \'\'moving-force\'\' problem. The equation of motion in matrix form is formulated using Lagrangian approach and the assumed mode method. The effects of the presence of intermediate point constraints in reducing the fluctuation of the contact force between the mass and the beam and the possible separation of the mass from the beam are investigated. The equation of motion and the numerical results are expressed in dimensionless form. The numerical results presented are therefore applicable for a large combination of system parameters.

Key Words
moving mass, contact force, multiple supports, beam

Address
Lee HP, NATL UNIV SINGAPORE,DEPT MECH & PROD ENGN,10 KENT RIDGE CRESCENT,SINGAPORE 0511,SINGAPORE

Abstract
A mathematical model of a cable as a system of interacting wires with interwire friction taken into account is presented in this paper. The effect of friction forces and the interwire slip on the mechanical properties of tension cables is investigated. it is shown that the slip occurs due to the twisting and bending deformations of wires, and it occurs in the form of micro-slips at the contact patches and macro-slips along the cable. The latter slipping starts near the terminals and propagates towards the middle of the cable with the increase of tension, and its propagation is proportional to the load. As the result of dry friction, the load-elongation characteristics of the cable become quadratic. The energy losses during the extension are shown to be proportional to the cube of the load and in inverse proportion to the friction force, a result qualitatively similar to that for lap joints. Presented examples show that the model is in qualitative agreement with the known experimental data.

Key Words
cable mechanics, energy losses, interwire friction

Address
Huang XL, WITTKE WASTE EQUIPMENT,MEDICINE HAT,AB T1C 1K6,CANADA
UNIV CALGARY,DEPT MECH ENGN,CALGARY,AB T2N 1N4,CANADA

Abstract
A model of a cable comprising interacting wires with dry friction forces at the interfaces is subjected to a quasi-static cyclic loading. The first cycle of this process, comprising of axial loading, unloading and reloading is investigated analytically. Explicit load-elongation relationships are obtained for all of the above phases of the cycle. An expression for the hysteretic losses is also obtained in an explicit form. It is shown that losses are proportional to the third power of the amplitude of the oscillating axial force, and are in inverse proportion to the interwire friction forces. The results obtained are used to introduce a model of a cable as a solid rod with an equivalent stiffness and damping properties of the rod material. It is shown that the stiffness of the equivalent rod is weakly nonlinear, whereas the viscous damping coefficient is proportional to the amplitude of the oscillation. Some numerical results illustrating the effect of cable parameters on the losses are given.

Key Words
cable mechanics, cyclic loading, dry friction, hysteresis

Address
Huang XL, WITTKE WASTE EQUIPMENT,MEDICINE HAT,AB T1C 1K6,CANADA
UNIV CALGARY,DEPT MECH ENGN,CALGARY,AB T2N 1N4,CANADA


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