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CONTENTS
Volume 7, Number 6, December 2007
 


Abstract
An optimal design method in cooperated with nonlinear inelastic analysis is presented. The proposed nonlinear inelastic method overcomes the difficulties due to incompatibility between the elastic global analysis and the limit state member design in the conventional LRFD method. The genetic algorithm used is a procedure based on Darwinian notions of survival of the fittest, where selection, crossover, and mutation operators are used to look for high performance ones among sections in the database. They are satisfied with the constraint functions and give the lightest weight to the structure. The objective function taken is the total weight of the steel structure and the constraint functions are load-carrying capacity, serviceability, and ductility requirement. Case studies of a planar portal frame, a space two-story frame, and a three-dimensional steel arch bridge are presented.

Key Words
nonlinear inelastic analysis; optimal design; genetic algorithm.

Address
Seung-Eock Kim; Department of Civil & Environmental Engineering, Construction Technical Research Institute, Sejong University, Seoul, Korea
Sang-Soo Ma; Korea Infrastructure Safety and Technology Corporation, Korea

Abstract
The torsional stiffness of bars with L,?,+,I, and cross-section In literature for thin-walled sections with L,?,+,I, and - shapes the approximate torsion equations for stiffness are used which were proposed by Bach (Hsu 1984), p.30. New formulae for torsional stiffness of bars with L,?,+,I, and cross section valid not only for thin-walled sections are presented in this paper. These formulae are obtained by appropriate polynomial approximation of stiffness results obtained by means of method of fundamental solutions. On the base of obtained results the validity of Bach?s formulae are verified when cross section is not thin-walled.

Key Words
elastic torsion; torsional stiffness formulae; method of fundamental solution; polynomial approximation; L, ?,+,I, and cross sections.

Address
Piotr Gorzelanczyk; Higher Vocational State School Pila, Polytechnic Institute, ul. Podchora? z.ych 10, 64-920 Pi l a, Poland
Henryk Tylicki; University of Technology and Life Science in Bydgoszcz, Faculty of Mechanical Engineering, Kaliskiego 7, 85-796 Bydgoszcz, Poland
Jan A. Kolodziej;
Institute of Applied Mechanics, Poznan University of Technology, ul. Piotrowo 3, 60-965 Poznan, Poland

Abstract
Analytical and experimental investigation on dynamic properties of extra lightweight concrete sandwich beams reinforced with various lay ups of carbon reinforced epoxy polymer composites (CFRP) are discussed. The lightweight concrete used in the core of the sandwich beams was made up of extra lightweight aggregate, Lica. The density of concrete was half of that of the ordinary concrete and its compressive strength was about 100 Kg/cm2. Two extra lightweight unreinforced (control) beams and six extra lightweight sandwich beams with various lay ups of CFRP were clamped in one end and tested under an impact load. The dimension of the beams without considering any reinforcement was 20 cm ?10 cm ?1.4 m. These were selected to ensure that the effect of shear during the bending test would be minimized. Three other beams, made up of ordinary concrete reinforced with steel bars, were tested in the same conditions. For measuring the damping capacity of sandwich beams three methods, Logarithmic Decrement Analysis (LDA), Hilbert Transform Analysis (HTA) and Moving Block Analysis (MBA) were applied. The first two methods are in time domain and the last one is in frequency domain. A comparison between the damping capacity of the beams obtained from all three methods, shows that the damping capacity of the extra lightweight concrete decreases by adding the composite reinforced layers to the upper and lower sides of the beams, and becomes most similar to the damping of the ordinary beams. Also the results show that the stiffness of the extra lightweight concrete beams increases by adding the composite reinforced layer to their both sides and become similar to the ordinary beams.

Key Words
extra lightweight concrete; CFRP; damping; sandwich beams; clamped beams.

Address
M. Naghipour; Department of Civil Engineering, Mazandaran University, Babol, Iran
M. Mehrzadi; Department of Civil Engineering, Islamic Azad University (IAU), Noor Branch, Iran

Abstract
The paper is concerned with the behavior of tapered steel plate girders, primarily subjected to shear loading; experimental as well as finite element results obtained from the studies are presented in this paper. In the experimental study, 11 large-scale girders, one of uniform section and 10 tapered, were tested to failure and all girders were analysed by finite element method. The results are compared and the accuracy of the finite element modeling established. A parametric study was carried out with thickness of web, loading direction and taper angle as parameters. An analytical model, based on Cardiff model for girders of uniform cross-section, is also proposed in the paper.

Key Words
plate girder; taper angle; experiment; finite element modelling; ultimate load behaviour; tension field action.

Address
N. E. Shanmugam; Department of Civil and Structural Engineering, Universiti Kebangsaan Malaysia, Bangi, Malaysia
Hu Min; Department of Civil Engineering, National University of Singapore, Singapore

Abstract
In recent decades there has been a trend towards improved mechanical characteristics of materials used in footbridge construction. It has enabled engineers to design lighter, slender and more aesthetic structures. As a result of these construction trends, many footbridges have become more susceptible to vibrations when subjected to dynamic loads. In addition to this, some inherit modelling uncertainties related to a lack of information on the as-built structure, such as boundary conditions, material properties, and the effects of non-structural elements make difficult to evaluate modal properties of footbridges, analytically. For these purposes, modal testing of footbridges is used to rectify these problems after construction. This paper describes an arch type steel footbridge, its analytical modelling, modal testing and finite element model calibration. A modern steel footbridge which has arch type structural system and located on the Karadeniz coast road in Trabzon, Turkey is selected as an application. An analytical modal analysis is performed on the developed 3D finite element model of footbridge to provide the analytical frequencies and mode shapes. The field ambient vibration tests on the footbridge deck under natural excitation such as human walking and traffic loads are conducted. The output-only modal parameter identification is carried out by using the peak picking of the average normalized power spectral densities in the frequency domain and stochastic subspace identification in the time domain, and dynamic characteristics such as natural frequencies mode shapes and damping ratios are determined. The finite element model of footbridge is calibrated to minimize the differences between analytically and experimentally estimated modal properties by changing some uncertain modelling parameters such as material properties. At the end of the study, maximum differences in the natural frequencies are reduced from 22% to only %5 and good agreement is found between analytical and experimental dynamic characteristics such as natural frequencies, mode shapes by model calibration.

Key Words
dynamic characteristics; finite element model calibration; footbridge; modal testing; peak picking; stochastic subspace identification.

Address
Karadeniz Technical University, Department of Civil Enginecring, 61080, Trabzon, Turkey


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