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CONTENTS
Volume 28, Number 2, January30 2008
 

Abstract
This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do
not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the
implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

Key Words
stochastic differential equation; stochastic finite element method(SFEM); spectral SFEM; Karhunen-Loeve expansion; Neumann expansion; Bernoulli-beam equation; stiffness matrix; bending rigidity; Exponential covariance model; Triangular covariance model; Wiener model.

Address
Hussein A.: Higher Technical Institute, 10th of Ramadan City, Basic Sciences Department, Egypt
El-Tawil M., El-Tahan W. and Mahmoud, A. A.: Engineering Mathematics Department, Faculty of Engineering, Cairo University, Giza, Egypt

Abstract
This paper suggests the use of wavelet multiresolution analysis (WMRA) and neural network for generation of artificial earthquake accelerograms from target spectrum. This procedure uses the
learning capabilities of radial basis function (RBF) neural network to expand the knowledge of the inverse mapping from response spectrum to earthquake accelerogram. In the first step, WMRA is used to
decompose earthquake accelerograms to several levels that each level covers a special range of frequencies, and then for every level a RBF neural network is trained to learn to relate the response
spectrum to wavelet coefficients. Finally the generated accelerogram using inverse discrete wavelet transform is obtained. An example is presented to demonstrate the effectiveness of the method.

Key Words
artificial accelerogram; wavelet transform; RBF neural network; target spectrum.

Address
G. Ghodrati Amiri and A. Bagheri: Center of Excellence for Fundamental Studies in Structural Engineering, College of Civil Engineering, Iran University of Science & Technology, PO Box 16765-163, Narmak, Tehran 16846, Iran

Abstract
This study is concerned with the establishment of the characteristic equation of a combined system consisting of a cantilever beam with a tip mass and an in-span visco-elastic helical spring-mass,
considering the mass of the helical spring. After obtaining the ?exact? characteristic equation of the combined system, by making use of a boundary value problem formulation, the characteristic equation is established via a transfer matrix method, as well. Further, the characteristic equation of a reduced system is obtained as a special case. Then, the characteristic equations are numerically solved for various combinations of the physical parameters. Further, comparison of the results with the massless spring case and the case in which the spring mass is partially considered, reveals the fact that neglecting or considering the mass of the spring partially can cause considerable errors for some combinations of the physical parameters of the system.

Key Words
combined systems; axial vibrations; bending vibrations; visco-elastic continuum; springmass attachment; effect of spring mass; free vibrations.

Address
M. Gurgoze, S. Zeren and M. M. A. Bicak: Faculty of Mechanical Engineering, Technical University of Istanbul, 34439, Gumu suyu, Istanbul, Turkey

Abstract
In several design codes and specifications, simplified formulae and charts are given for determining the effective lengths of frame columns. It is shown that these formulae may yield rather
erroneous results in certain cases. This is due to the fact that, the code formulae utilise only local stiffness distributions. In this paper, a simplified procedure for determining approximate values for the buckling loads of braced frames is developed. The procedure utilises a fictitious load analysis of frames and yields errors less than 10%, which may be considered suitable for design purposes. The proposed procedure is applied to several numerical examples and it is shown that all the errors are in the acceptable range.

Key Words
buckling load; buckling length; effective length; non-sway mode; braced frames; isolated subassembly; multi-storey frames; design codes.

Address
Konuralp Girgin and Gunay Ozmen: Faculty of Civil Engineering, Istanbul Technical University, Maslak 34469, Istanbul, Turkey

Abstract
The shear lag has been studied for many years. Nevertheless, existing research gives a variety of stress concentration factors. Unlike the elementary beam theory, the application of load is not unique in reality. For example, concentrated load can be applied as point load or distributed load along the height of the web. This non-uniqueness may be a reason for the discrepancy of the stress
concentration factors in the existing studies. The finite element method has been often employed for studying the effect of the shear lag. However, not many researches have taken into account the influence
of the finite element mesh on the shear lag phenomenon, although stress concentration can be quite sensitive to the mesh employed in the finite element analysis. This may be another source for the
discrepancy of the stress concentration factors. It also needs to be noted that much less studies seem to have been conducted for the shear lag effect on deflection while some design codes have formulas. The
present study investigates the shear lag effect in a simply supported box girder by the three-dimensional finite element method using shell elements. The whole girder is modeled by shell elements, and extensive
parametric study with respect to the geometry of a box girder is carried out. Not only stress concentration but also deflection is computed. The effect of the way load is applied and the dependency of finite element mesh on the shear lag are carefully treated. Based on the numerical results thus obtained, empirical formulas are proposed to compute stress concentration and deflection that includes the shear lag effect.

Key Words
shear lag; simply supported box girders; stress concentration; deflection; three-dimensional finite element analysis.

Address
Eiki Yamaguchi: Dept. of Civil Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan
Taweep Chaisomphob and Jaturong Sa-nguanmanasak:
School of Civil Engineering and Technology, Sirindhorn International Institute of Technology, Thammasat University, PO Box. 22, Thammasat-Rangsit Post Office, Pathum thani 12121, Thailand
Chartree Lertsima: Asian Engineering Consultants Corp., 21st Fl., Sathorn Nakorn Tower Bldg., 100/34-35 North Sathorn Rd., Bangkok 10500, Thailand

Abstract
Numerical solution to buckling analysis of beams and columns are obtained by the method of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for various support conditions considering the variation of flexural rigidity. The solution technique is applied to find the buckling load of fully or partially embedded columns such as piles. A simple semi- inverse method of DQ or HDQ is
proposed for determining the flexural rigidities at various sections of non-prismatic column ( pile) partially and fully embedded given the buckling load , buckled shape and sub-grade reaction of the soil. The obtained results are compared with the existing solutions available from other numerical methods and analytical results. In addition, this paper also uses a recently developed technique, known as the differential transformation (DT) to determine the critical buckling load of fully or partially supported heavy prismatic piles as well as fully supported non-prismatic piles. In solving the problem, governing differential equation is converted to algebraic equations using differential transformation methods (DT) which must be solved together with applied boundary conditions. The symbolic programming package, Mathematica is ideally suitable to solve such recursive equations by considering fairly large number of terms.

Key Words
column; stability; embedded piles; differential quadrature; semi-inverse approach; differential transformation.

Address
S. Rajasekaran: Infrastructure Engineering, PSG College of Technology, Coimbatore . 641004, Tamilnadu, India

Abstract
Double-sided punched metal plate timber fasteners present projections on both sides, which offer improved joint fire resistance and better joint aesthetics. In this paper, 3-D nonlinear finite element models were developed to simulate double-sided nail plate fastener timber joints. The models, incorporating orthotropic elasticity, Hill?s yield criterion and elasto-plasticity and contact algorithms, are capable of simulating complex contact between the tooth and the timber and between the base plate and the timber in a fastener. Using validated models, parametric studies of the double-sided nail plate joints was undertaken to cover the tooth length and the tooth width. Optimal configuration was assumed to have been attained when increase in nail plate tooth width did not result in a raise in joint capacity, in conjunction with the optimum tooth length. This paper presents the first attempt to model and optimise tooth profile of double-sided nail plate fastener timber joints, which offers rational designs of such fasteners.

Key Words
contact; double-sided nail plate fastener; finite element; parametric study; rational design.

Address
Tinozivashe Zhou: School of the Environment, University of Brighton, Moulsecoomb, Lewes Road, Brighton, East Sussex, BN2 4GJ, United Kingdom
Z. W. Guan: Dept. of Engineering, The University of Liverpool, Brownlow Hill, Liverpool, L69 3GQ, United Kingdom

Abstract
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Key Words
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Address
Bo Wun Huang, Pu Ping Yu and Jwo Ming Jou: Dept. of Mechanical Engineering, Cheng Shiu University, 840 Cheng Ching Rd. Niaosung, 833, Kaohsiung, Taiwan

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