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CONTENTS
Volume 42, Number 4, May25 2012
 

Abstract
For generally damped linear systems with repeated eigenvalues and defective eigenvectors, this study provides a decomposition method based on residue matrix, which is suitable for engineering applications. Based on this method, a hybrid approach is presented, incorporating the merits of the modal superposition method and the residue matrix decomposition method, which does not need to consider the defective characteristics of the eigenvectors corresponding to repeated eigenvalues. The method derived in this study has clear physical concepts and is easily to be understood and mastered by engineering designers. Furthermore, this study analyzes the applicability of step-by-step methods including the Newmark beta and Runge-Kutta methods for dynamic response calculation of defective systems. Finally, the implementation procedure of the proposed hybrid approach is illustrated by analyzing numerical examples, and the correctness and the effectiveness of the formula are judged by comparing the results obtained from the different methods.

Key Words
damped system; repeated eigenvalues; transfer function; residue matrix; modal superposition method; defective system

Address
Rui-fang Yu: Institute of Geophysics, China Earthquake Administration, Beijing, P.R. China
Xi-yuan Zhou: Beijing University of Technology, Beijing, P.R. China
Mei-qiao Yuan: Institute of Earthquake Engineering, Chongqing, P.R. China

Abstract
An efficient one dimensional finite element model has been presented for the dynamic analysis of composite laminated beams, using the efficient layerwise zigzag theory. To meet the convergence requirements for the weak integral formulation, cubic Hermite interpolation is used for the transverse displacement (w0), and linear interpolation is used for the axial displacement (u0) and shear rotation (x0). Each node of an element has four degrees of freedom. The expressions of variationally consistent inertia, stiffness matrices and the load vector are derived in closed form using exact integration. The formulation is validated by comparing the results with the 2D-FE results for composite symmetric and sandwich beams with various end conditions. The employed finite element model is free of shear locking. The present zigzag finite element results for natural frequencies, mode shapes of cantilever and clamped–clamped beams are obtained with a one-dimensional finite element codes developed in MATLAB. These 1D-FE results for cantilever and clamped beams are compared with the 2D-FE results obtained using ABAQUS to show the accuracy of the developed MATLAB code, for zigzag theory for these boundary conditions. This comparison establishes the accuracy of zigzag finite element analysis for dynamic response under given boundary conditions.

Key Words
composite laminates; FEM, MATLAB; dynamic analysis; ABAQUS

Address
M. Naushad Alam, Nirbhay Kr. Upadhyay and Mohd. Anas: Department of Mechanical Engineering, Aligarh Muslim University, Aligarh-202002, India

Abstract
In this study, it is aim to perform the construction stage analysis of suspension bridges using time dependent material properties. Fatih Sultan Mehmet Suspension Bridge connecting the Europe and Asia in Istanbul is selected as an example. Finite element models of the bridge are modelled using SAP2000 program considering project drawing. Geometric nonlinearities are taken into consideration in the analysis using P-Delta large displacement criterion. The time dependent material strength variations and geometric variations are included in the analysis. Because of the fact that the bridge has steel structural system, only prestressing steel relaxation is considered as time dependent material properties. The structural behaviour of the bridge at different construction stages has been examined. Two different finite element analyses with and without construction stages are carried out and results are compared with each other. As analyses result, variation of the displacement and internal forces such as bending moment, axial forces and shear forces for bridge deck and towers are given with detail. It is seen that construction stage analysis has remarkable effect on the structural behaviour of the bridge.

Key Words
construction stage analysis Fatih Sultan Mehmet Suspension Bridge; finite element analysis; time dependent material properties

Address
Murat Gunaydin: Civil Engineering Department, Gumu hane University, 29000, Trabzon, Turkey
Suleyman Adanur, Ahmet Can Altunisik: Civil Engineering Department, Karadeniz Technical University, 61080, Trabzon, Turkey
Baris Sevim: Civil Engineering Department, Yildiz Technical University, 34220, Istanbul, Turkey

Abstract
Age-related problems especially corrosion and fatigue are normally suffered by weatherworn ships and aging offshore structures. The effect of corrosion is one of the important factors in the Common Structural Rule (CSR) guideline of the ship design based on a 20 or 25 years design life. The aim of this research is the clarification of the corrosion effect on ultimate strength of stiffened panels on various types of double hull oil tankers. In the case of ships, corrosion is a phenomenon caused by the ambient environment and it has different characteristics depending on the parts involved. Extensive research considering these characteristic have already done by previous researchers. Based on this data, the ultimate strength behavior of stiffened panels for four double hull oil tankers such as VLCC, Suezmax, Aframax, and Panamax classes are compared and analyzed. By considering hogging and sagging bending moments, the stiffened panels of the deck, inner bottom and outer bottom located far away from neutral axis of ship are assessed. The results of this paper will be useful in evaluating the ultimate strength of an oil tanker subjected to corrosion. These results will be an informative example to check the effect of ultimate strength of a stiffened panel according to corrosion addition from CSR for a given type of ship.

Key Words
corrosion; ultimate strength; stiffened panel; double hull oil tankers; common structural rule; time-dependent corrosion wastage model

Address
Do Kyun Kim, Dae Kyeom Park, Jeong Hwan Kim, Sang Jin Kimb, Bong Ju Kim, Jung Kwan Seo and Jeom Kee Paik: The Ship and Offshore Research Institute (The Lloyd\'s Register Educational Trust Research Centre of Excellence), Pusan National University, Busan, Korea

Abstract
Numerous oil tanker losses have been reported and one of the possible causes of such casualties is caused by the structural failure of aging ship hulls in rough weather. In aging ships, corrosion and fatigue cracks are the two most important factors affecting structural safety and integrity. This research is about effect on hull girder ultimate strength behavior of double hull oil tanker according to corrosion after Part I: stiffened panel. Based on corrosion data of Part I (time-dependent corrosion wastage model and CSR corrosion model), when progressing corrosion of fourtypes of double hull oil tankers (VLCC, Suezmax, Aframax, and Panamax), the ultimate strength behavior of hull girder is compared and analyzed. In case of the ultimate strength behavior of hull girder, when occurring corrosion, the result under vertical and horizontal bending moment is analyzed. The effect of time-dependent corrosion wastage on the ultimate hull girder strength as well as the area, section modulus, and moment of inertia are also studied. The result of this research will be useful data to evaluate ultimate hull girder strength of corroded double hull oil tanker.

Key Words
corrosion; ultimate strength; hull girder; double hull oil tankers; common structural rule; time-dependent corrosion wastage model

Address
Do Kyun Kim, Dae Kyeom Park, Dong Hee Park, Han Byul Kim, Bong Ju Kim, Jung Kwan Seo and Jeom Kee Paik: The Ship and Offshore Research Institute (The Lloyd\'s Register Educational Trust Research Centre of Excellence), Pusan National University, Busan, Korea

Abstract
An experimental program was carried out to investigate the influence of fibre reinforcement on the mechanical behaviour of high strength reinforced concrete beams. Eighteen beams, loaded in fourpoint bending tests, were examined by applying monotonically increasing controlled displacements and recording the response in terms of load-deflection curves up to failure. The major test variables were the volume fraction of steel fibres and the transverse steel amount for two different values of shear span. The contribution of the stirrups to the shear strength was derived from the deformations of their vertical legs, measured by means of strain gauges. The structural response of the tested beams was analyzed to evaluate strength, stiffness, energy absorption capacity and failure mode. The experimental results and observed behaviour are in good agreement with those obtained by other authors, confirming that an adequate amount of steel fibres in the concrete can be an alternative solution for minimizing the density of transverse reinforcement. However, the paper shows that the use of different theoretical or semi-empirical models, available in literature, leads to different predictions of the ultimate load in the case of dominant shear failure mode.

Key Words
high strength concrete beam; steel fibres; stirrups; experimental study

Address
Calogero Cucchiara: Dipartimento di Ingegneria Civile, Ambientale e Aeronautica, Universita di Palermo, Palermo, Italy
Marinella Fossetti: Facolta di Ingegneria e Architettura, Universita di Enna \"Kore\", Enna, Italy
Maurizio Papia: Dipartimento di Ingegneria Civile, Ambientale e Aeronautica, Universita di Palermo, Palermo, Italy

Abstract
This paper presents results of a numerical analysis performed on a corrugated steel plate (CSP) bridge during a backfilling process. The analysed bridge structure was a box culvert having a span of 12315 mm as well as a clear height of 3550 mm. Obtained calculation results were compared with the experimental ones. The paper is presented with the application of the Fast Lagrangian Analysis of Continua (FLAC) program based on the finite differences method (FDM) to determine behaviour of the soil-steel bridge structure during backfilling. The assumptions of a computational 2D model of soil-steel structure with a non-linear interface layer are described. Parametric analysis of the interface element is also given in order to receive the most realistic calculation results. The method based on this computational model may be used with large success to design calculations of this specific type of structure instead of the conventional and fairly inaccurate analytical methods. The conclusions drawn from such analysis can be helpful mostly for the assessment of the behaviour of steel-soil bridge structures under loads of backfilling. In consideration of an even more frequent application of this type of structure, conclusions from the conducted analysis can be generalized to a whole class of similar structural bridge solutions.

Key Words
soil-structure interactions; soil-steel bridge; steel corrugated plate; finite difference method; backfilling

Address
Damian Beben: Faculty of Civil Engineering, Opole University of Technology, Katowicka Street 48, 45-061 Opole, Poland

Abstract
In this study, the effect of in-plane deformations on the dynamic behavior of laminated plates is investigated. For this purpose, the displacement-time and strain-time histories obtained from the large deflection analysis of laminated plates are compared for the cases with and without including in-plane deformations. For the first one, in-plane stiffness and inertia effects are considered when formulating the dynamic response of the laminated composite plate subjected to the blast loading. Then, the problem is solved without considering the in-plane deformations. The geometric nonlinearity effects are taken into account by using the von Karman large deflection theory of thin plates and transverse shear stresses are ignored for both cases. The equations of motion for the plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The effects of the magnitude of the blast load, the thickness of the plate and boundary conditions on the in-plane deformations are investigated.

Key Words
large deflection; blast loading; in-plane effects; laminated plate; geometric nonlinearity

Address
Zafer Kazanci: Aerospace Engineering Department, Turkish Air Force Academy, 34149, Ye ilyurt, Istanbul, Turkey
Halit S. Turkmen: Faculty of Aeronautics and Astronautics, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey


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