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CONTENTS
Volume 42, Number 1, April10 2012
 

Abstract
In this study, Pasternak foundation model, which is a two parameter foundation model, is used to analyze the behavior of laterally loaded beams embedded in semi-infinite media. Total potential energy variation of the system is written to formulate the problem that yielded the required field equations and the boundary conditions. Shear force discontinuities are exposed within the boundary conditions by variational method and are validated by photo elastic experiments. Exact solution of the deflection of the beam is obtained. Both foundation parameters are obtained by self calibration for this particular problem and loading type in this study. It is shown that, like the first parameter k, the second foundation parameter G also depends not only on the material type but also on the geometry and the loading type of the system. On the other hand, surface deflection of the semi infinite media under singular loading is obtained and another method is proposed to determine the foundation parameters using the solution of this problem.

Key Words
Pasternak foundation; variational method; photo elastic method; experimental method for Pasternak constants; boundary conditions; sub grade; two parameter foundation

Address
A.Yalcin Akoz: Engineering Faculty, Civil Engineering Department, T.C. Maltepe University, Istanbul, Turkey
Hale Ergun: Civil Engineering Faculty, Civil Engineering Department, ITU, Istanbul, Turkey

Abstract
There are a large number of papers in the literature dealing with the free vibration analysis of single/multi-span uniform beam with multiple spring-mass systems, but that of coupled multi-span beams carrying spring-mass attachments is rare. In this note, free vibration analysis of a weakly coupled beam system with spring-mass attachments is conducted. The mode localization and frequency loci veering phenomena of the coupled beam system are investigated. Studies show that for weakly coupled beam system with spring-mass attachments, the mode localization and frequency loci veering will occur once there is a disorder in the system.

Key Words
vibration; coupled beam system; mode localization; frequency loci veering

Address
M. Huang: Research Center of Intelligent Transportation System, Sun Yat-sen University, Guangzhou, Guangdong Province, 510006, P.R. China
J.K. Liu and Z.R. Lu: Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou, Guangdong Province, 510006, P.R. China

Abstract
Recently, investigated failures of external post-tensioned (PT) tendons have called attention to the corrosion of strands in PT bridges, and the prevention of ongoing corrosion is required to secure their structural integrity. Since voids inside ducts can be a source for the ingress of water or deleterious chemicals, the vacuum grouting (VG) method and a volumeter for estimating amount of repair grouts were employed to fill voided ducts. However, the VG method is expensive and time-consuming for infield application because it requires an air-tight condition of entire ducts. Thus, latest research assessed three different repair grouting methods, and the pressure vacuum grouting (PVG) method was recommended in the field because it showed good filling capability in voided ducts and did not require an air-tight condition. Thus, a new method is required to estimate the volume of repair grouts because the PVG method is not applied in air-tight ducts. This research assesses the relationship between voided areas on ducts identified with soundings and required grout volume for repair using experimental results. The results show that the proposed equations and assumptions for estimating repair grout volume provide a sufficient amount of repair grouts for filling voided ducts.

Key Words
post-tensioned bridge; void; repair grouting; volume of repair grouts; sounding inspection

Address
Seok Been Im: Bridge/Structure Part, Civil ENG Center, Samsung C&T, 1327-1, Seocho-Dong, Seocho-Gu, Seoul 137-858, Korea
Stefan Hurlebaus: Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX77843, USA

Abstract
This paper presents an alternative way to derive the exact element stiffness matrix for a beam on Winkler foundation and the fixed-end force vector due to a linearly distributed load. The element flexibility matrix is derived first and forms the core of the exact element stiffness matrix. The governing differential compatibility of the problem is derived using the virtual force principle and solved to obtain the exact moment interpolation functions. The matrix virtual force equation is employed to obtain the exact element flexibility matrix using the exact moment interpolation functions. The so-called \"natural\" element stiffness matrix is obtained by inverting the exact element flexibility matrix. Two numerical examples are used to verify the accuracy and the efficiency of the natural beam element on Winkler foundation.

Key Words
beam elements; winkler foundation; finite element; flexibility-based formulation; virtual force principle; soil-structure interaction; natural stiffness matrix

Address
Suchart Limkatanyu: Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University,
Songkhla, 90110, Thailand
Kittisak Kuntiyawichai: Department of Civil Engineering, Faculty of Engineering, Ubonratchathani University,
Ubonratchathani, Thailand
Enrico Spacone: Department of PRICOS, Faculty of Architecture, University \"G. D\'Annunzio\", Pescara, Italy
Minho Kwon: Department of Civil Engineering, ERI, Gyeongsang National University, Jinju, Korea

Abstract
Precast-cast insitu concrete bridge construction is widely practiced for small to medium span structures. These bridges consist of precast pre-stressed concrete beams of various cross-sections with a cast in-situ reinforced concrete slab. The connection between the beams and the slab is via shear links often included during the manufacturing process of the beams. This form of construction is attractive as it provides for standardisation, reduced formwork and construction time. The assessment of the integrity of shear connectors in existing bridges is a major challenge. A procedure for assessment of shear connectors based on vibration testing and finite element model updating is proposed. The technique is applied successfully to a scaled model bridge model and an existing bridge structure.

Key Words
shear connectors; structural integrity assessment; composite structures; vibration testing; partial composite action

Address
Pilate Moyo, Bongani Sibanda and Hans Beushausen: Department of Civil Engineering, University of Cape Town, Cape Town, South Africa

Abstract
With an active structural involvement in spiral case structure (SCS) that is always the design and research focus of hydroelectric power plant (HPP), the compressible membrane sandwiched between steel spiral case and surrounding reinforced concrete was often assumed to be linear elastic material in conventional design analysis of SCS. Unfortunately considerable previous studies have proved that the foam material serving as membrane exhibits essentially nonlinear mechanical behavior. In order to clarify the effect of membrane (foam) material\'s nonlinear stress-strain behavior on SCS, this work performed a case study on SCS with a compressible membrane using the ABAQUS code after a sound calibration of the employed constitutive model describing foam material. In view of the successful capture of fitted stress-strain curve of test by the FEM program, we recommend an application and dissemination of the simulation technique employed in this work for membrane material description to structural designers of SCS. Even more important, the case study argues that taking into account the nonlinear stress-strain response of membrane material in loading process is definitely essential. However, we hold it unnecessary to consider the membrane material\'s hysteresis and additionally, employment of nonlinear elastic model for membrane material description is adequate to the structural design of SCS. Understanding and accepting these concepts will help to analyze and predict the structural performance of SCS more accurately in design effort.

Key Words
spiral case structure; compressible membrane; foam material; nonlinear stress-strain behavior; hydroelectric power plant

Address
Qi-Ling Zhang: Changjiang River Scientific Research Institute, 430010 Wuhan, Hubei, China
He-Gao Wu: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, 430072 Wuhan, Hubei, China

Abstract
In this paper, forced vibration differential equations of motion of Euler-Bernoulli beams with different boundary conditions and dynamic loads are solved using differential transform method (DTM), analytical solutions. Then, the modal deflections of these beams are obtained. The calculated modal deflections using DTM are represented in tables and depicted in graphs and compared with the results of the analytical solutions where a very good agreement is observed.

Key Words
differential transform method; forced vibration; partial differential equations; natural frequencies

Address
Seval Catal: Department of Civil Engineering, Faculty of Engineering (Applied Mathematics), Dokuz Eylul University, Izmir, Turkey

Abstract
All contemporary seismic Codes have adopted smooth design acceleration response spectra, which have derived by statistical analysis of many elastic response spectra of natural accelerograms. The above smooth design spectra are characterized by two main branches, an horizontal branch that is 2.5 times higher than the peak ground acceleration, and a declining parabolic branch. According to Eurocode EN/1998, the period range of the horizontal, flat branch is extended from 0.1 s, for rock soils, up to 0.8 s for softer ones. However, from many natural recorded accelerograms of important earthquakes, the real spectral amplification factor appears to be much higher than 2.5 and this means that the spectrum leads to an unsafe seismic design of the structures. This point is an issue open to question and it is the object of the present study. In the present paper, the spectral amplification factor of the smooth design acceleration spectra is re-calculated on the grounds of a known \"reliability index\" for a desired probability of exceedance. As a pilot scheme, the seismic area of Greece is chosen, as it is the most seismically hazardous area in Europe. The accelerograms of the 82 most important earthquakes, which have occurred in Greece during the last 38 years, are used. The soil categories are taken into account according to EN/ 1998. The results that have been concluded from these data are compared with the results obtained from other strong earthquakes reported in the World literature.

Key Words
maximum spectral amplification factor; effective spectral amplification factor; standard normal probability density function; probability of exceeding; reliability index; predominant period; Eurocode EN/1998

Address
Triantafyllos K. Makarios: Institute of Engineering Seismology and Earthquake Engineering, 5 Ag Georgiou Str, GR 55535 Patriarchika Pylaias, Thessaloniki, Greece


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