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CONTENTS
Volume 6, Number 4, June 1998
 

Abstract
The stiffness matrix of a two-dimensional contact surface element is deduced from the principle of virtual work. The incremental loading procedure used is controlled by displacement and stress. Special potential contact elements are used to avoid the need to rearrange the FEM mesh due to variations of the contact surface as contact develops. Published results are used to validate the method, which is then applied to a turbine to solve the contact problem between the blade root and rotor in the region in which a \'push fit\' connects the blade to its rotor.

Key Words
elastic contact, contact surface element, potential contact element

Address
Liu ZX, Shanghai Jiao Tong Univ, Dept Engn Mech, Shanghai 200030, Peoples R China
Shanghai Jiao Tong Univ, Dept Engn Mech, Shanghai 200030, Peoples R China
Univ Wales, Cardiff Sch Engn, Div Struct Engn, Cardiff CF2 3TB, S Glam, Wales

Abstract
Slit shear walls an reinforced concrete shear wall structures with purposely built-in vertical slits. If the slits are inserted with visco-elastic damping materials, the shear walls will become viscoelastic sandwich beams. When adequately designed, this kind of structures can be quite effective in resisting earthquake loads. Herein, a simple analysis method is developed for the evaluation of the stochastic responses of visco-elastic slit shear walls. In the proposed method, the stiffness and mass matrices are derived by using Rayleigh-Ritz method, and the responses of the structures are calculated by means of complex modal analysis. Apart from slit shear walls, this analysis method is also applicable to coupled shear walls and cantilevered sandwich beams. Numerical examples are presented and the results clearly show that the seismic responses of shear wall structures can be substantially reduced by incorporating vertical slits into the walls and inserting visco-elastic damping materials into the slits.

Key Words
shear wall, sandwich beam, vibration, damping, modal analysis, stochastic response analysis

Address
Kwan AKH, Univ Hong Kong, Dept Civil & Struct Engn, Pokfulam Rd, Hong Kong, Peoples R China
Univ Hong Kong, Dept Civil & Struct Engn, Hong Kong, Peoples R China
Chinese Acad Sci, Inst Mech, Beijing 100864, Peoples R China

Abstract
This paper concerns the development and implementation of an orthotropic, stress resultant elasto-plastic finite element model for the collapse load analysis of reinforced concrete plates. The model implements yield line plasticity theory for reinforced concrete. The behaviour of the yield functions are studied, and modifications introduced to ensure a robust finite element model of cases involving bending and twisting stress resultants (M-x, M-y, M-xy). Onset of plasticity is always governed by the general yield-line-model (YLM), but in some cases a switch to the stress resultant form of the von Mises function is used to ensure the proper evolution of plastic strains. Case studies are presented, involving isotropic and orthotropic plates, to assess the behaviour of the yield line approach. The YLM function is shown to perform extremely well, in predicting both the collapse loads and failure mechanisms.

Key Words
yield line model, orthotropic plasticity, stress-resultant yield function, reinforced concrete plates, plastic node method

Address
Rasmussen LJ, Ramboll Consulting Engineers, Bredevej 2, DK-2830 Virum, Denmark
Ramboll Consulting Engineers, DK-2830 Virum, Denmark
Univ Queensland, Dept Civil Engn, Brisbane, Qld 4072, Australia

Abstract
The effective length factor of a framed column may be determined by means of the alignment chart procedure. This method is based on many unrealistic assumptions, among which is that all columns have the same stiffness parameter, which is dependent on the length, axial load, and moment of inertia of the column. A new approximate method is developed for the determination of effective length factors for columns in unbraced frames. This method takes into account the effects of inelastic column behaviour, far end conditions of the restraining beams and columns, semi-rigid beam-to-column connections, and differentiated stiffness parameters of columns. This method may be implemented on a microcomputer. A numerical study was carried out to demonstrate the extent to which the involved parameters affect the K factor. The beam-to-column connection stiffness, the stiffness parameter of columns, and the far end conditions of restraining members have a significant effect on the K factor of the column under investigation. The developed method is recommended for design purposes.

Key Words
unbraced frames, stability, design, columns, effective length factor, inelastic behaviour, concrete frames, steel frames, buckling

Address
Essa HS, Ain Shams Univ, Dept Civil Engn, Cairo, Egypt
Ain Shams Univ, Dept Civil Engn, Cairo, Egypt

Abstract
Flat plate constructions are structural systems which are directly placed on columns without any beams. Various solution methods have been introduced for the solution of flat plate structures under horizontal and vertical loads. In most of these solution methods, models comprising of one column and one plate have been studied. In other solutions, however, co-behavior of two reciprocal columns has been investigated. In this study, interrelations of all the columns on one storey have been examined. At the end of the study structure consisting of nine columns and four plates has been chosen as a model. Then unit moment has been successively applied to each of these columns and unit moments carried over the other columns have been found. By working out solutions far plates and columns varying in ratio, carry-over factors have been found and these factors given in tables. In addition, fixed-end moment factors on the columns arising due to vertical load were also calculated. Then citing slope-deflection equations to which these results could be applied, some examples of moment and horizontal equilibrium equations have been given.

Key Words
flat plate, equivalent frame

Address
Unluoglu E, Univ Osmangazi, Dept Civil Engn, Eskisehir, Turkey
Univ Osmangazi, Dept Civil Engn, Eskisehir, Turkey

Abstract
A three-dimensional static nonlinear finite element analysis was performed on the NUPEC large-scale flanged shear wall, which was the subject of an international study program. Details of the constitutive models and analysis procedures used are provided, and the results of the analysis are presented and discussed. The analytical results are compared to the experimentally observed behaviour, and reasonable correlation is observed. Deficiencies in the modelling are identified. In addition, a parametric study is undertaken to investigate factors and mechanisms influencing both the observed behaviour and the calculated response. Finally, a cyclic load analysis of the wall is described and discussed. The paper serves to point out aspects in modelling that are critical to both producing realistic results, and correctly interpreting those results.

Key Words
analysis, behaviour, cyclic, finite element, nonlinear, reinforced concrete, shear, structure, test, wall

Address
Vecchio FJ, Univ Toronto, Dept Civil Engn, 35 St George St, Toronto, ON M5S 1A4, Canada
Univ Toronto, Dept Civil Engn, Toronto, ON M5S 1A4, Canada

Abstract
The dynamic response of an elastic torsion shaft of revolution is analysed by the Line-Loaded Integral Equation Method (LLIEM). A \"Dynamic Point Ring Couple\" (DPRC) is used as a fictitious fundamental load and is distributed in an elastic space along the axis of the shaft outside the shaft occupation. According to the boundary condition, our problem is reduced to a 1-D Fredholm integral equation of the first kind, which is simpler for solving than that of a 2-D singular integral equation of the same kind obtanied by Boundary Element Method (BEM), for steady periodically varied loading. Numerical example of a shaft with quadratic generator under sinusoidal type of torque is given. Formulas for stresses and dangerous frequency are mentioned.


Key Words
torsion of shaft of revolution, elastodynamic analysis, the line-loaded integral equation method

Address
Yun TQ, S China Univ Technol, Dept Mech, Guangzhou 510641, Peoples R China
S China Univ Technol, Dept Mech, Guangzhou 510641, Peoples R China

Abstract
A mathematical model is developed to predict the fatigue notch factor of butt welds subject to number of parameters such as weld geometry, residual stresses under dynamic combined loading conditions (tensile and bending). Linear elastic fracture mechanics, finite element analysis, dimensional analysis and superposition approaches are used for the modelling. The predicted results are in good agreement with the available experimental data. As a result, scatters of the fatigue data can be significantly reduced by plotting S-N curve as (S . K-f) vs. N.

Key Words
fatigue notch factor, stress intensity factor, crack propagation, weld geometry, residual stress and butt welded joints

Address
Univ Adelaide, Adelaide, SA 5005, Australia


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