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CONTENTS
Volume 43, Number 5, September10 2012
 

Abstract
Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of nonprismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

Key Words
vibration frequency; variable axial force; non-prismatic beam; buckling load; weak form integral equation

Address
H. Saffari: Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
M. Mohammadnejad: Department of Civil Engineering, Birjand University of Technology, Birjand, Iran
M.H. Bagheripour: Department of Civil Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract
This paper presents a spatial catenary cable element for the nonlinear analysis of cablesupported structures. An incremental-iterative solution based on the Newton-Raphson method is adopted for solving the equilibrium equation. As a result, the element stiffness matrix and nodal forces are determined, wherein the effect of self-weight and pretension are taken into account. In the case of the initial cable tension is given, an algorithm for form-finding of cable-supported structures is proposed to determine precisely the unstressed length of the cables. Several classical numerical examples are solved and compared with the other available numerical methods or experiment tests showing the accuracy and efficiency of the present elements.

Key Words
cable; cable-stayed bridge; catenary; geometric nonlinear analysis; nonlinear static analysis; cable pre-tension; long-span bridges; coupled flutter; multi-mode analysis; state space method

Address
Tan-Van Vu: Faculty of Civil Engineering, Ho Chi Minh City University of Architecture, Vietnam
Hak-Eun Lee: Civil, Environmental & Architectural Engineering, Korea University, 5-1, Anam-dong, Sungbuk-go,
Seoul 136-701, Korea
Quoc-Tinh Bui: Department of Civil Engineering, University of Siegen, Germany

Abstract
The Expo Culture Centre is one of the permanent buildings at the World Expo 2010 in Shanghai, China. The main structure has an oval shape and consists of 36 radial cantilever steel trusses with different lengths and inner frames made of concrete-filled rectangular steel tube members. Tuned mass dampers are used to reduce the excessive vibrations of the sixth floor that are caused by humaninduced resonance. A three-dimensional analytical model of the system is developed, and its main characteristics are established. A series of field tests are performed on the structure, and the test results show that the vertical vibration frequencies of most structural cantilevers are between 2.5 Hz and 3.5 Hz, which falls in the range of human-induced vibration. Twelve pairs of tuned mass dampers weighing 115 tons total were installed in the structure to suppress the vibration response of the system. These mass dampers were tuned to the vertical vibration frequency of the structure, which had the highest possibility of excitation. Test data obtained after the installation of the tuned mass dampers are used to evaluate their effectiveness for the reduction of the vibration acceleration. An analytical model of the structure is calibrated according to the measured dynamic characteristics. An analysis of the modified model is performed and the results show that when people walk normally, the structural vibration was low and the tuned mass dampers have no effect, but when people run at the structural vibration frequency, the tuned mass dampers can reduce the floor vibration acceleration by approximately 15%.

Key Words
Expo Culture Centre; steel truss; cantilever; human-induced vibration; serviceability; tuned mass damper

Address
Xilin Lu, Kun Ding, Weixing Shi and Dagen Weng: State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China

Abstract
The aim of the current work is to describe the flexural behaviour of simply supported concrete beams with tension reinforcement spliced at mid-span. The parameters included in the study were the type of the concrete, the splice length and the configuration of the hooked splice. Fifteen beams were cast using an ordinary concrete mix and two fiber reinforced concrete mixes incorporating steel and polypropylene fibers. Each concrete mix was used to cast five beams with continuous, spliced and hooked spliced tension steel bars. A test beam was reinforced on the tension side with two 12 mm bars and the splice length was 20 and 40 times the bar diameter. The hooked bars were spliced along 20 times the bar diameter and provided with 45-degree and 90-degree hooks. The test results in terms of cracking and ultimate loads, cracking patterns, ductility, and failure modes are reported. The results demonstrated the consequences due to short splices and the improvement in the structural behaviour due to the use of hooks and the confinement provided by the steel and polypropylene fibers.

Key Words
bond; splice; hook; fiber reinforced concrete; steel fibers; polypropylene fibers

Address
Mohamed A. Safan: Civil Engineering Department, Faculty of Engineering, Menoufia University, Shebeen El-Koom, 1111 Menoufia, Egypt

Abstract
In this study, stochastic responses of a cable-stayed bridge subjected to the spatially varying earthquake ground motion are investigated by the finite element method taking into account soil-structure interaction (SSI) effects. The considered bridge in the analysis is Quincy Bay-view Bridge built on the Mississippi River in between 1983-1987 in Illinois, USA. The bridge is composed of two H-shaped concrete towers, double plane fan type cables and a composite concrete-steel girder deck. In order to determine the stochastic response of the bridge, a two-dimensional lumped masses model is considered. Incoherence, wave-passage and site response effects are taken into account for the spatially varying earthquake ground motion. Depending on variation in the earthquake motion, the response values of the cable-stayed bridge supported on firm, medium and soft foundation soil are obtained, separately. The effects of SSI on the stochastic response of the cable-stayed bridge are also investigated including foundation as a rigidly capped vertical pile groups. In this approach, piles closely grouped together beneath the towers are viewed as a single equivalent upright beam. The soil-pile interaction is linearly idealized as an upright beam on Winkler foundation model which is commonly used to study the response of single piles. A sufficient number of springs on the beam should be used along the length of the piles. The springs near the surface are usually the most important to characterize the response of the piles surrounded by the soil; thus a closer spacing may be used in that region. However, in generally springs are evenly spaced at about half the diameter of the pile. The results of the stochastic analysis with and without the SSI are compared each other while the bridge is under the sway of the spatially varying earthquake ground motion. Specifically, in case of rigid towers and soft soil condition, it is pointed out that the SSI should be significantly taken into account for the design of such bridges.

Key Words
soil-structure interaction; cable-stayed bridge; piles; spatially varying earthquake ground motion; stochastic analysis

Address
Zeliha Kuyumcua and Sevket Ates: Department of Civil Engineering, Karadeniz Technical University, Trabzon, 61080, Turkey

Abstract
The mismatch of ply orientations in composite laminates can cause high interlaminar stress concentrations near the free edges. Evaluation of these interlaminar stresses and their role in the progressive damage analysis of laminates is desirable. Recently, the authors developed a new method to relate the physically based micromechanics approach with the meso-scale CDM considering matrix cracking and induced delamination. In this paper, the developed method is applied for the analysis of edge effects in various angle-ply laminates such as [10/−10]2s, [30/−30]2s and [45/−45]2s and comparing the results with available traditional CDM and experimental results. It is shown that the obtained stress-strain behaviors of laminates are in good agreement with the available experimental results and even in better agreement than the traditional CDM results. Variations of the stresses and stiffness components through the laminate thickness and near the free edges are also computed and compared with the available CDM results.

Key Words
micro-meso; edge effects; progressive damage; continuum damage

Address
H. Hosseini-Toudeshky: Department of Aerospace Engineering, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, Iran
A. Farrokhabadi: Department of Aerospace Engineering, Semnan University, Semnan, Iran
B. Mohammadi: School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran

Abstract
A new concept sea-floating port called mobile harbor has been introduced, in order to resolve the limitation of current above-ground port facilities against the continuous growth of worldwide marine transportation. One of important subjects in the design of a mobile harbor is to secure the dynamic stability against wave-induced excitation, because a relatively large-scale heavy crane system installed at the top of mobile harbor should load/unload containers at sea under the sea state up to level 3. In this context, this paper addresses a two-step sequential analytical-numerical method for analyzing the structural dynamic response of the mobile harbor crane system to the wave-induced rolling excitation. The rigid ship motion of mobile harbor by wave is analytically solved, and the flexible dynamic response of the crane system by the rigid ship motion is analyzed by the finite element method. The hydrodynamic effect between sea water and mobile harbor is reflected by means of the added moment of inertia.

Key Words
mobile harbor; roll-out roll-in (RORI) crane; wave-induced excitation; rigid ship roll motion; structural dynamic response; finite element analysis

Address
Jin-Rae Cho: School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea; Research & Development Institute of Midas IT, Gyeonggi-Do 463-400, Korea
Ki-Chul Han: School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea
Soon-Wook Hwang: School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea
Choon-Soo Cho: School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea
O-Kaung Lim: School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea

Abstract
This paper provides a variety of viewpoints to illustrate the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges. Based on the smooth and convergent bridge shapes obtained by the initial shape analysis, the one-element cable system (OECS) and multi-element cable system (MECS) models of the Kao Ping Hsi Bridge in Taiwan are developed to verify the applicability of the analytical model and numerical formulation from the field observations in the authors\' previous work. For this purpose, the modal analysis of the two finite element models are conducted to calculate the natural frequency and normalized mode shape of the individual modes of the bridge. The modal coupling assessment is also performed to obtain the generalized mass ratios among the structural components for each mode of the bridge. The findings indicate that the coupled modes are attributed to the frequency loci veering and mode localization when the \"pure\" deck-tower frequency and the \"pure\" stay cable frequency approach one another, implying that the mode shapes of such coupled modes are simply different from those of the deck-tower system or stay cables alone. The distribution of the generalized mass ratios between the deck-tower system and stay cables are useful indices for quantitatively assessing the degree of coupling for each mode. These results are demonstrated to fully understand the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges.

Key Words
cable-stayed bridge; deck-stay interaction; initial shape analysis; one-element cable system; multi-element cable system

Address
Ming-Yi Liu, Li-Chin Lin and Pao-Hsii Wang: Department of Civil Engineering, Chung Yuan Christian University, Jhongli City, Taoyuan County 32023, Taiwan


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