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CONTENTS
Volume 7, Number 2, February 1999
 

Abstract
This paper deals with the development of an approach for evaluating the squash load and rigidity of unprotected concrete filled steel columns at elevated temperatures. The current approach of evaluating these properties is reviewed. It is shown that with a non-uniform temperature distribution, over the composite cross-section, the calculations for the squash load and rigidity are tedious in the current method. A simplified approach is proposed to evaluate the temperature distribution, squash load, and rigidity of composite columns. This approach is based on the model in Eurocode 4 and can conveniently be used to calculate the resistance to axial compression of a concrete filled steel column for any fire resistance time. The accuracy of the proposed approach is assessed by comparing the predicted strengths against the results of fire tests on concrete filled circular and square steel columns. The applicability of the proposed approach to a design situation is illustrated through a numerical example.

Key Words
fire resistance calculation, failure loads, HSS columns, concrete filled, steel columns, squash load evaluation, high temperature properties

Address
Wang YC, Bldg Res Estab, Struct Design Div, Watford WD2 7JR, England
Bldg Res Estab, Struct Design Div, Watford WD2 7JR, England
Natl Res Council Canada, Inst Res Construct, Natl Fire Lab, Ottawa, ON, Canada

Abstract
An analytical methodology for solving antiplane problem of anisotropic materials is proposed and discussed in detail in this study. The material considered in this study possesses a symmetry plane at z=0. The relationship between the problems of anisotropic materials and the corresponding isotropic problems are established by Ma (1996) on the basis of the general solutions for the shear stresses and displacement in both the polar and Cartesian coordinate systems. This implies that any solution of an anisotropic problem can be obtained by solving a corresponding isotropic problem. In this study some examples and numerical results are presented as an explanation of how the complicated anisotropic problem could be solved by the associated simpler isotropic problem.


Key Words
antiplane problem, anisotropic materials, shear stresses

Address
Ma CC, Natl Taiwan Univ, Dept Mech Engn, Taipei 10764, Taiwan
Natl Taiwan Univ, Dept Mech Engn, Taipei 10764, Taiwan

Abstract
The present paper shows a new non-tensorial approach to derive basic equations for various structural analyses. It can be used directly in numerical computation procedures. The aim of the paper is, however, to show that the approach serves as an excellent tool for analytical purposes also, working as a link between analytical and numerical techniques. The paper gives a method to derive, at first, expressions for strains in general beam and shell analyses, and secondly, the governing equilibrium equations. The approach is based on the utilization of local fixed Cartesian coordinate systems. Applying these, all the definitions required are the simple basic ones, well-known from the analyses in common global coordinates. In addition, the familiar principle of virtual work has been adopted. The method will be, apparently, most powerful in teaching the theories of curved beam and shell structures for students not familiar with tensor analysis. The final results obtained have no novelty value in themselves, but the procedure developed opens through its systematic and graphic progress a new standpoint to theoretical considerations.

Key Words
fundamental structural mechanics, curved structures, local coordinate systems, equilibrium equations, principle of virtual work

Address
Paavola J, Helsinki Univ Technol, Lab Struct Mech, POB 2100, FIN-02015 HUT, Finland
Helsinki Univ Technol, Lab Struct Mech, FIN-02015 HUT, Finland

Abstract
Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are studied. The shell is simply supported at both ends. The highly coupled partial differential equations are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resulting differential equations are solved by Galerkin finite element method, In this solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and higher order shear deformation theory (HSD) become higher for a symmetric laminations than their unsymmetric counterpart. That is due to the effect of bending-streching coupling. It is also found that due to the discontinuity of inplane stresses at the interface of the laminate, the slope of transverse normal and shear stresses aren\'t continuous across the interface. For free vibration analysis, through dividing each layer into thin laminas, the variable coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle-ply are generally higher than their antisymmetric counterpart. Also the results are in good agreement with similar results found in literatures.

Key Words
elasticity solution, laminated, orthotropic, free vibrations, dynamic loading, cylindrical shell

Address
Shakeri M, Amirkabir Univ Technol, Dept Engn Mech, Hafez Ave 424, Tehran, Iran
Amirkabir Univ Technol, Dept Engn Mech, Tehran, Iran

Abstract
A previously proposed finite element formulation method is refined and modified to generate a new type of elements. The method is based on selecting a set of general solution modes for element formulation. The constant strain modes and higher order modes are selected and the formulation method is designed to ensure that the element will pass the basic single element test, which in turn ensures the passage of the basic patch test. If the element is to pass the higher order patch test also, the element stiffness matrix is in general asymmetric. The element stiffness matrix depends only on a nodal displacement matrix and a nodal force matrix. A symmetric stiffness matrix can be obtained by either modifying the nodal displacement matrix or the nodal force matrix. It is shown that both modifications lead to the same new element, which is demonstrated through numerical examples to be more robust than an assumed stress hybrid element in plane stress application. The method of formulation can also be used to arrive at the conforming displacement and hybrid stress formulations. The convergence of the latter two is explained from the point of view of the proposed method.

Key Words
patch test, convergence, element formulation, asymmetric stiffness matrix, higher order performance

Address
Mau ST, New Jersey Inst Technol, Newark Coll Engn, Newark, NJ 07102 USA
New Jersey Inst Technol, Newark Coll Engn, Newark, NJ 07102 USA
Univ Houston, Houston, TX 77204 USA

Abstract
A semi-stochastic process model of reliability was established for hyperbolic cooling towers subjected to combined loadings of wind force, self-weight, temperature loading. Effect of the soil-structure interaction on reliability was evaluated. By involving the gust factor, an equivalent static scheme was employed to convert the dynamic model to static model. The TR combination rule was used to consider relations between load responses. An analysis example was made on the 90M cooling tower of Maoming, Guangdong of China. Numerical results show that the design not including interaction turns to be conservative.

Key Words
cooling tower reliability, interaction, TR load combination rule

Address
Liao W, Tongji Univ, Dept Bridge Engn, Shanghai 200092, Peoples R China
Tongji Univ, Dept Bridge Engn, Shanghai 200092, Peoples R China
Shanghai Inst Mech Engn, Shanghai 200092, Peoples R China

Abstract
This paper presents a mechanistic approach to uniaxial viscoelastic constitutive modeling of asphalt concrete that accounts for damage evolution under cyclic loading conditions. An elasticviscoelastic correspondence principle in terms of pseudo variables is applied to separately evaluate viscoelasticity and time-dependent damage growth in asphalt concrete. The time-dependent damage growth in asphalt concrete is modeled by using a damage parameter based on a generalization of microcrack growth law. Internal state variables that describe the hysteretic behavior of asphalt concrete are determined. A constitutive equation in terms of stress and pseudo strain is first established for controlled-strain mode and then transformed to a controlled-stress constitutive equation by simply replacing physical stress and pseudo strain with pseudo stress and physical strain. Tensile uniaxial fatigue tests are performed under the controlled-strain mode to determine model parameters. The constitutive equations in terms of pseudo strain and pseudo stress satisfactorily predict the constitutive behavior of asphalt concrete all the way up to failure under controlled-strain and -stress modes, respectively.

Key Words
asphalt concrete, correspondence principle, constitutive model, cyclic test, damage, fatigue, viscoelasticity

Address
Lee HJ, Kangnung Natl Univ, Dept Civil Engn, Kangnung 210702, South Korea
Kangnung Natl Univ, Dept Civil Engn, Kangnung 210702, South Korea
N Carolina State Univ, Dept Civil Engn, Raleigh, NC 27695 USA
Youngdong Univ, Dept Civil Engn, Chungbuk 370800, South Korea


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