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CONTENTS
Volume 22, Number 2, January30 2006
 

Abstract
Exact analytical solutions for in-plane static problems of planar curved beams with variable curvatures and variable cross-sections are derived by using the initial value method. The governing equations include the axial extension and shear deformation effects. The fundamental matrix required by the initial value method is obtained analytically. Then, the displacements, slopes and stress resultants are found analytically along the beam axis by using the fundamental matrix. The results are given in analytical forms. In order to show the advantages of the method, some examples are solved and the results are compared with the existing results in the literature. One of the advantages of the proposed method is that the high degree of statically indeterminacy adds no extra difficulty to the solution. For some examples, the deformed shape along the beam axis is determined and plotted and also the slope and stress resultants are given in tables.

Key Words
curved beam; variable cross-section; axial extension; shear deformation; initial value method.

Address
Istanbul Technical University, Faculty of Mechanical Engineering, Gumussuyu 34437, Istanbul, Turkey

Abstract
A p-version of the finite element method in conjunction with the modeling dynamic method using the arc-length stretch deformation is considered to determine the bending natural frequencies of a cantilever flexible plate mounted on the periphery of a rotating hub. The plate Fourier p-element is used to set up the linear equations of motion. The transverse displacements are formulated in terms of cubic polynomials functions used generally in FEM plus a variable number of trigonometric shapes functions representing the internals DOF for the plate element. Trigonometric enriched stiffness, mass and centrifugal stiffness matrices are derived using symbolic computation. The convergence properties of the rotating plate Fourier p-element proposed and the results are in good agreement with the work of other investigators. From the results of the computation, the influences of rotating speed, aspect ratio, Poisson? ratio and the hub radius on the natural frequencies are investigated.

Key Words
Fourier p-element; stretch displacement; gyroscopic effect; rotating plates.

Address
Department of Mechanical Engineering, Faculty of Engineering Sciences, University Abou Bekr Belkaid, 13000, Tlemcen, Algeria

Abstract
A close form solution of the maximum deflection for cracked columns with rectangular cross-sections was developed and thus the elastic buckling behavior and ultimate bearing capacity were studied analytically. First, taking into account the effect of the crack in the potential energy of elastic systems, a trigonometric series solution for the elastic deflection equation of an arbitrary crack position was derived by use of the Rayleigh-Ritz energy method and an analytical expression of the maximum deflection was obtained. By comparison with the rotational spring model (Okamura et al. 1969) and the equivalent stiffness method (Sinha et al. 2002), the advantages of the present solution are that there are few assumed conditions and the effect of axial compression on crack closure was considered. Second, based on the above solutions, the equilibrium paths of the elastic buckling were analytically described for cracked columns subjected to both axial and eccentric compressive load. Finally, as examples, the influence of crack depth, load eccentricity and column slenderness on the elastic buckling behavior was investigated in the case of a rectangular column with a single-edge crack. The relationship of the load capacity of the column with respect to crack depth and eccentricity or slenderness was also illustrated. The analytical and numerical results from the examples show that there are three kinds of collapse mechanisms for the various states of cracking, eccentricity and slenderness. These are the bifurcation for axial compression, the limit point instability for the condition of the deeper crack and lighter eccentricity and the fracture for higher eccentricity. As a result, the conception of critical transition eccentricity (e/ h)c , from limit-point buckling to fracture failure, was proposed and the critical values of (e/h)c were numerically determined for various eccentricities, crack depths and slenderness.

Key Words
equilibrium path; elastic buckling; bearing capacity; cracked column; eccentricity; slenderness.

Address
L. Zhou(1,2) and Y. Huang(1)
(1)Department of Civil Engineering, Xi?n University of Architecture Technology, Xi?n 710055, P. R. China
(2)Department of Civil Engineering, Wuyi University, Jiangmen 529020, P. R. China

Abstract
Nowadays it is very necessary to generate artificial accelerograms because of lack of adequate earthquake records and vast usage of time-history dynamic analysis to calculate responses of structures. According to the lack of natural records, the best choice is to use proper artificial earthquake records for the specified design zone. These records should be generated in a way that would contain seismic properties of a vast area and therefore could be applied as design records. The main objective of this paper is to present a new method based on wavelet theory to generate more artificial earthquake records, which are compatible with target spectrum. Wavelets are able to decompose time series to several levels that each level covers a specific range of frequencies. If an accelerogram is transformed by Fourier transform to frequency domain, then wavelets are considered as a transform in time-scale domain which frequency has been changed to scale in the recent domain. Since wavelet theory separates each signal, it is able to generate so many artificial records having the same target spectrum.

Key Words
wavelet theory; artificial accelerogram; target spectrum; frequency content.

Address
Center of Excellence for Fundamental Studies in Structural Engineering, Department of Civil Engineering, Iran University of Science & Technology, P.O. Box 16765-163, Narmak, Tehran 16844, Iran

Abstract
In this paper, the non-linear time-dependent closed-form, discrete and combined solutions for the post-elastic response of a geometrically and physically non-linear suspended cable to a uniformly distributed load considering the creep effects, are presented. The time-dependent closed-form method for the particularly straightforward determination of a vertical uniformly distributed load applied over the entire span of a cable and the accompanying deflection at time t corresponding to the elastic limit and/or to the elastic region, post-elastic and failure range of a suspended cable is described. The actual stress-strain properties of steel cables as well as creep of cables and their rheological characteristics are considered. In this solution, applying the Irvine? theory, the direct use of experimental data, such as the actual stress-strain and strain-time properties of high-strength steel cables, is implemented. The results obtained by the closed-form solution, i.e., a load corresponding to the elastic limit, post-elastic and failure range at time t, enable the direct use in the discrete non-linear time-dependent post-elastic analysis of a suspended cable. This initial value of load is necessary for the non-linear time-dependent elastic and post-elastic discrete analysis, concerning incremental and iterative solution strategies with tangent modulus concept. At each time step, the suspended cable is analyzed under the applied load and imposed deformations originated due to creep. This combined time-dependent approach, based on the closed-form solution and on the FEM, allows a prediction of the required load that occurs in the post-elastic region. The application of the described methods and derived equations is illustrated by numerical examples.

Key Words
suspended cable; time-dependent post-elastic analysis; creep of cable; non-linear analysis; closed-form analysis; discrete combined analysis; stress-strain diagram of cable; elastic limit; deflection equation of cable.

Address
Faculty of Civil Engineering, Technical University of Kosice, Vysokoskolska 4, 042 00 Kosice, Slovak Republic

Abstract
Taking into account the geometrical and material nonlinearities, an ultimate behavior of reinforced concrete cooling tower shell in hyperbolic configuration is presented. The design wind pressures suggested in the guidelines of the US (ACI) and Germany (VGB), with or without the effect of internal suction, are employed in the analysis to examine the qualitative and quantitative characteristics of each design wind pressure. The geometrical nonlinearity is incorporated by the Green-Lagrange strain tensor. The nonlinear features of concrete, such as the nonlinear stress-strain relation in compression, the tensile cracking with the smeared crack model, an effect of tension stiffening, are taken into account. The biaxial stress state in concrete is represented by an improved work-hardening plasticity model. From the perspective of quality of wind pressures, the two guidelines are determined as highly correlated each other. Through the extensive analysis on the Niederaussem cooling tower in Germany, not only the ultimate load is determined but also the mechanism of failure, distribution of cracks, damage processes, stress redistributions, and mean crack width are examined.

Key Words
reinforced concrete cooling tower; nonlinearity; ultimate load; design guidelines; damage index.

Address
Hyuk-Chun Noh; Department of Civil Engineering and Engineering Mechanics, Columbia University, New York 10027, USA
Chang-Koon Choi; Department of Civil and Environmental Engineering, KAIST, Daejeon 305-701, Korea

Abstract
NiTi-wire shape memory alloy (SMA) dampers, that utilize NiTi SMA wires to simultaneously damp tension, compression and torsion, was developed for structural control implementation in this study. First, eight reduced-scale NiTi-wire SMA dampers were constructed. Then tension, compression and torsion experiments using the eight reduced-scale NiTi-wire SMA dampers of different specification were done. The experimental results revealed all of the eight reduced-scale NiTi-wire SMA dampers had the ability to simultaneously supply tension-compression damping and torsion damping. Finally, mechanics analysis of the NiTi-wire SMA dampers was done based on a model of the SMA-wire restoring force and on tension-compression and torsion damping analysis. The damping analytical results were found to be similar to the damping experimental results.

Key Words
shape memory alloys (SMA); smart materials; smart structures; damper; structural control; vibration; earthquake.

Address
College of Civil Engineering, Southeast University, Nanjing City 210096, P. R. China


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