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CONTENTS
Volume 15, Number 1, January 2003
 

Abstract
This paper presents the formulation of a new bridge-vehicle system with validation using the field data. Both pitching and twisting modes of the vehicle are considered in the contribution of the dynamic effects in the bridge responses. A heavy vehicle was hired as a control vehicle with known axle weight, axle spacing and spring coefficients. The measured responses were generated from the control
vehicle running at a particular speed at a test span at Ma Tau Wai Flyover. The measured responses were acquired using strain gauges installed beneath the girder beams of the test bridge. The simulated responses were generated using BRVEAN that is a self-developed program based on the proposed bridge-vehicle
system. The validation shows that the bridge model is valid for representing the test bridge and the governing equations are valid for representing the motion of moving vehicles.

Key Words
bridge-vehicle interaction; dynamic responses; eccentric beam model; Fast Fourier Transform; field test; impact on bridges; surface roughness; tire-suspension system.

Address
Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hunghom, Kolwoon, Hong Kong
Blasting and Vibration Research Department, Yangtze River Scientific Research Institute, 23 Huangpu Street, Wuhan, Hubei, 430010, P.R. China
T.Y. Lin, Hong Kong, Consulting Engineers Ltd., Hong Kong
Wong and Ouyang (Civil & Structural Engineering) Ltd., Hong Kong

Abstract
The formulation of a new bridge-vehicle system using shell with eccentric beam elements has been introduced in a companion paper (Part I). The new system takes into account of the contribution of the twisting and pitching modes of vehicles to the bridge responses. It can also be used to study the dynamic transverse load distribution of a bridge. This paper presents a parametric study on the impact induced by one vehicle or multi-vehicle running across a bridge using the proposed model. Several parameters were considered as variables including the mass ratio, the speed parameter, the frequency ratio and the axle spacing parameter to investigate their effects on the impact factor. A total number of 189
cases were carried out in this parametric study. Within the realistic range of vehicle considered, the maximum impact factors could be 2.24, 1.78 and 1.49 for bridges with spans 10 m, 20 m and 30 m respectively.

Key Words
axle spacing parameter; bridge-vehicle interaction; dynamic transverse load distribution; frequency ratio; impact factor; mass ratio; speed parameter; transverse impact factor.

Address
Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hunghom, Kolwoon, Hong Kong
Blasting and Vibration Research Department, Yangtze River Scientific Research Institute, 23 Huangpu Street, Wuhan, Hubei, 430010, P.R. China
T.Y. Lin, Hong Kong, Consulting Engineers Ltd., Hong Kong
Wong and Ouyang (Civil & Structural Engineering) Ltd., Hong Kong

Abstract
A computer program has been developed for the optimum design of prestressed concrete beams under flexure. Optimum values of prestressing force, tendon configuration, and cross-sectional dimensions are determined subject to constraints on the design variables and stresses. 28 constraints have been used including flexural stresses, cover requirement, the aspect ratios for top and bottom flanges and web part of a beam and ultimate moment. The objective function contains cost of concrete, prestressing force and formwork. Using this function, it is possible to obtain minimum cost design, minimum weight or cross-sectional area of concrete design and minimum prestressing force design. Besides the idealized Ishaped cross-section, which is widely used in literature, a general I-shaped cross-section with eight geometrical design variables are used here. Four examples, one of which is available in the literature and the others are modified form of it, have been solved for minimum cost and minimum cross-sectional area designs and the results are compared. The computer program, which employs modified grid search optimization method, can assist a designer in producing efficient designs rapidly and easily. Considerable savings in computational work are thus made possible.

Key Words
prestressed concrete beam design; modified grid search; optimum design; optimization; linear and non-linear programming and cost optimization.

Address
Department of Civil Engineering, Cukurova University, 01330 Adana, Turkey

Abstract
The motivation of this paper is to introduce the modern technology of large-scale cooling tower design. Thereby the innovative design concept for the world

Key Words
cooling tower; FE-simulation; structural damage; material modeling of RC.

Address
Institute for Structural Statics and Dynamics RWTH Aachen, Mies-van-der-Rohe-Strasse 1, D-52056 Aachen, Germany
Institute for Statics and Dynamics, Bergische Universit?t Wuppertal, Pauluskirchstrasse 7, D-42285 Wuppertal, Germany
Institute for Statics and Dynamics, Ruhr-Universit?t Bochum, Universit?tsstrasse 150, D-44780 Bochum, Germany

Abstract
The governing differential equation for buckling of a one-step bar with the effect of shear deformation is established and its exact solution is obtained. Then, the exact solution is used to derive the eigenvalue equation of a multi-step bar. The new exact approach combining the transfer matrix method and the closed form solution of one step bar is presented. The proposed methods is convenient for solving the entire and partial buckling of one-step and multi-step bars with various end conditions, with or without shear deformation effect, subjected to concentrated axial loads. A numerical example is given explaining the proposed procedure and investigating the effect of shear deformation on the critical buckling force of a multi-step bar.

Key Words
stability; buckling; shear deformation; bar.

Address
Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

Abstract
A new simple 3-node triangular flat-shell element with standard nodal DOF (6 DOF per node) is proposed for the linear and geometrically nonlinear analysis of very thin to thick plate and shell structures. The formulation of element GT9 (Long and Xu 1994), a generalized conforming membrane element with rigid rotational freedoms, is employed as the membrane component of the new shell
element. Both one-point reduced integration scheme and a corresponding stabilization matrix are adopted for avoiding membrane locking and hourglass phenomenon. The bending component of the new element comes from a new generalized conforming Kirchhoff-Mindlin plate element TSL-T9, which is derived in this paper based on semiLoof constrains and rational shear interpolation. Thus the convergence can be guaranteed and no shear locking will happen. Furthermore, a simple hybrid procedure is suggested to improve the stress solutions, and the Updated Lagrangian formulae are also established for the
geometrically nonlinear problems. Numerical results with solutions, which are solved by some other recent element models and the models in the commercial finite element software ABAQUS, are presented. They show that the proposed element, denoted as GMST18, exhibits excellent and better performance for the
analysis of thin-think plates and shells in both linear and geometrically nonlinear problems.

Key Words
finite element; flat-shell element; generalized conforming; semiLoof constrains geometrical nonlinear; UL formulation; GMST18.

Address
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
Department of Science & Art, China University of Mining & Technology, Beijing 100083, China

Abstract
The Ting Kau Bridge in Hong Kong is a cable-stayed bridge comprising two main spans and two side spans. The bridge deck is supported by three towers, an end pier and an abutment. Each of the three towers consists of a single reinforced concrete mast which reduces its section in steps, and it is strengthened by transverse cables and struts in the transverse vertical plane. The bridge deck is supported by four inclined planes of cables emanating from anchorages at the tower tops. In view of the threat from typhoons, the dynamic behaviour of long-span cable-supported bridges in the region is always an important consideration in their design. This paper is devoted to the ambient vibration measurements of the bridge for evaluation of dynamic characteristics including the natural frequencies and mode shapes. It also describes the modelling of the bridge. A few finite element models are developed and calibrated to match with the field data and the results of subsequent structural health monitoring of the bridge.

Key Words
bridges; cables & tendons; composite structures; concrete structures; dynamics; steel structures.

Address
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
Department of Civil Engineering, South China University of Technology, Guangzhou, China
Tsing Ma Control Area Division, Highways Department, The Government of the Hong Kong
Special Administrative Region, China

Abstract
The bubble packing method is implemented for adaptive mesh generation in two and three dimensions. Bubbles on the boundary of a three-dimensional domain are controlled independently of the interior bubbles in the domain, and a modified octree technique is employed to place initial bubbles in the three-dimensional zone. Numerical comparisons are made with other mesh generation techniques to demonstrate the effectiveness of the present bubble packing scheme for two- and three-dimensional domains. It is shown that this bubble packing method provides a high quality of mesh and affordable control of mesh density as well.

Key Words
mesh generation; bubble packing method; modified octree; error estimator; mesh density function.

Address
Department of Mechanical Engineering (ME3028), Korea Advanced Institute of Science and Technology, Science Town, DaeJeon 305-701, South Korea

Abstract
A new approach to the analysis of horizontally curved beams is presented in this paper. The proposed method simplifies a two-dimensional structure into a one-dimensional structure just like a normal beam for structural analysis and, therefore, reduces the computational effort significantly.

Key Words
curved beam; finite element; force method; stiffness method.

Address
College of Engineering, National University of Defense Science and Technology,Changsha, Hunan 410003, P.R. China
Department of Civil Engineering and Architecture, University of Foshan,18 Jiang Wan Road, Foshan City, Guangdong 528000, P.R. China
Department of Building and Construction, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong


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