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CONTENTS
Volume 38, Number 6, June25 2011
 

Abstract
Assessing the ductility of reinforced concrete sections and members has been a complex and intractable problem for many years. Given the complexity in estimating ductility, members are often designed specifically for strength whilst ductility is provided implicitly through the use of ductile steel reinforcing bars and by ensuring that concrete crushing provides the ultimate limit state. As such, the empirical hinge length and neutral axis depth approaches have been sufficient to estimate ductility and moment redistribution within the bounds of the test regimes from which they were derived. However, being empirical, these methods do not have a sound structural mechanics background and consequently have severe limitations when brittle materials are used and when concrete crushing may not occur. Structural mechanics based approaches to estimating rotational capacities and rotation requirements for given amounts of moment redistribution have shown that FRP plated reinforced concrete (RC) sections can have significant moment redistribution capacities. In this paper, the concept of moment redistribution in beams is explained and it is shown specifically how an existing RC member can be retrofitted with FRP plates for both strength and ductility requirements. Furthermore, it is also shown how ductility through moment redistribution can be used to maximise the increase in strength of a member. The concept of primary and secondary hinges is also introduced and it is shown how the response of the nonhinge region influences the redistribution capacity of the primary hinges, and that for maximum moment redistribution to occur the non-hinge region needs to remain elastic.

Key Words
reinforced concrete; moment redistribution; member ductility; fibre reinforced polymer; FRP; plated structure; hinge; member strength

Address
Deric John Oehlers, Matthew Haskett and Mohamed Ali M.S.: School of Civil, Environmental and Mining Engineering, University of Adelaide, South Australia 5005, Australia

Abstract
A novel structural damage detection method with a new damage index has been recently proposed by the authors based on the statistical moments of dynamic responses of shear building structures subject to white noise ground motion. The statistical moment-based damage detection (SMBDD) method is theoretically extended in this paper with general application. The generalized SMBDD method is more versatile and can identify damage locations and damage severities of many types of building structures under various external excitations. In particular, the incomplete measurements can be considered by the proposed method without mode shape expansion or model reduction. Various damage scenarios of two general forms of building structures with incomplete measurements are investigated in consideration of different excitations. The effects of measurement noise are also investigated. The damage locations and damage severities are correctly identified even when a high noise level of 15% and incomplete measurements are considered. The effectiveness and versatility of the generalized SMBDD method are demonstrated.

Key Words
building structures; random excitation; statistical moments; incomplete measurements; damage location; damage severity; measurement noise

Address
J. Zhang: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong
Y.L. Xu: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong
Y. Xia: Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong
J. Li: College of Civil Engineering, Tongji University, Shanghai, China

Abstract
In the present study, a new kind of multivariable Reissner-Mindlin plate elements with two kinds of variables based on B-spline wavelet on the interval (BSWI) is constructed to solve the static and vibration problems of a square Reissner-Mindlin plate, a skew Reissner-Mindlin plate, and a Reissner-Mindlin plate on an elastic foundation. Based on generalized variational principle, finite element formulations are derived from generalized potential energy functional. The two-dimensional tensor product BSWI is employed to form the shape functions and construct multivariable BSWI elements. The multivariable wavelet finite element method proposed here can improve the solving accuracy apparently because generalized stress and strain are interpolated separately. In addition, compared with commonly used Daubechies wavelet finite element method, BSWI has explicit expression and a very good approximation property which guarantee the satisfying results. The efficiency of the proposed multivariable Reissner-Mindlin plate elements are verified through some numerical examples in the end.

Key Words
multivariable; B-spline wavelet on the interval; Reissner-Mindlin plate; static analysis; vibration analysis

Address
Xingwu Zhang, Xuefeng Chen and Zhengjia He: State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi\'an Jiaotong University, Xi\'an 710049, PR China

Abstract
The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

Key Words
composite piezoelectric transducer; electromechanical coupling; cylindrical structure; radial vibration; functionally graded material

Address
H.M. Wang, Y.K. Wei and Z.X. Xu: Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China

Abstract
Developers of new finite elements or nonlinear solution techniques rely on discriminative benchmark tests drawn from the literature to assess the advantages and drawbacks of new formulations. Buckling benchmark tests provide a rigorous evaluation of finite elements applied to thin structures, and a complete and detailed set of reference results would therefore prove very useful in carrying out such evaluations. Results are usually presented in the form of load-deflection curves that developers must reconstruct by extracting the points, a procedure which is often tedious and inaccurate. Moreover the curves are usually given without accompanying information such as the calculation time or number of iterations it took for the model to converge, even though this type of data is equally important in practice. This paper presents ten different limit-point buckling benchmark tests, and provides for each one the reference load-deflection curve, all the points necessary to recreate the curve in tabulated form, analysis data such as calculation time, number of iterations and increments, and all of the inputs used to obtain these results.

Key Words
finite element; nonlinear analysis; limit-point buckling benchmarks; post-buckling; pathfollowing strategy; large rotations

Address
Ion Leahu-Aluas: LEM3, UMR CNRS 7239, Arts et Metiers ParisTech, 4 rue A. Fresnel, 57078 Metz Cedex 03, France; Georgia Tech Lorraine, Georgia Institute of Technology, 2-3 rue Marconi, 57070 Metz, France
Farid Abed-Meraim: LEM3, UMR CNRS 7239, Arts et Metiers ParisTech, 4 rue A. Fresnel, 57078 Metz Cedex 03, France

Abstract
In this paper, the three dimensional Parallel Realistic Failure Process Analysis (RFPA3D-Parallel) code based on micromechanical model is employed to investigate the bonding behavior in FRP sheet bonded to concrete in single shear test. In the model, the heterogeneity of brittle disordered material at a meso-scale was taken into consideration in order to realistically demonstrate the mechanical characteristics of FRP-to-concrete. Modified Mohr-coulomb strength criterion with tension cut-off, where a stressed element can damage in shear or in tension, was adopted and a stiffness degradation approach was used to simulate the initiation, propagation and growth of microcracks in the model. In addition, a Master-Slave parallel operation control technique was adopted to implement the parallel computation of a large numerical model. Parallel computational results of debonding of FRP-concrete visually reproduce the spatial and temporal debonding failure progression of microcracks in FRP sheet bonded to concrete, which agrees well with the existing testing results in laboratory. The numerical approach in this study provides a useful tool for enhancing our understanding of cracking and debonding failure process and mechanism of FRP-concrete and our ability to predict mechanical performance and reliability of these FRP sheet bonded to concrete structures.

Key Words
FRP sheet; concrete; debonding; damage; failure process; parallel computation

Address
Tao Xu: Center for Material Failure Modeling Research, Dalian University, Dalian 116622, China; State Key Laboratory of Geo-hazard Prevention and Geo-environment Protection, Chengdu University of Technology, Chengdu 610059, China
Yongbin Zhang: School of Civil Engineering, Dalian University of Technology, Dalian 116024, China
Z.Z. Liang: School of Civil Engineering, Dalian University of Technology, Dalian 116024, China
Chun-an Tang: School of Civil Engineering, Dalian University of Technology, Dalian 116024, China
Jian Zhao: Ecole Polytechnique Federale de Lausanne, Rock Mechanics Laboratory, CH-1015 Lausanne, Switzerland

Abstract
This paper investigates the design using wind-moment method for semi-rigid un-braced steel frames bending on weak axis. A limiting sway method has been proposed to reduce the frame sway. Allowance for steel section optimization between moment of inertia on minor axis column and major axis beam was used in conjunction with slope-deflection analysis to derive equations for optimum design in the proposed method. A series of un-braced steel frames comprised of two, four, and six bays ranging in height of two and four storey were studied on minor axis framing. The frames were designed for minimum gravity load in conjunction with maximum wind load and vice-versa. The accuracy of the design equation was found to be in good agreement with linear elastic computer analysis up to second order analysis. The study concluded that the adoption of wind-moment method and the proposed limiting sway method for semi-rigid steel frame bending on weak axis should be restricted to low-rise frames not more than four storey.

Key Words
limiting sway method; partial strength connection; un-braced frame; weak axis; windmoment method

Address
Mahmood Md. Tahir and Shek Poi Ngian: Steel Technology Center, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia


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