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CONTENTS
Volume 16, Number 2, August 2003
 

Abstract
A novel finite element model based on the incremental endochronic theory with the effect of temperature was developed in this study to explore the deformed behaviors of a flexible pavement material. Three mesh systems and two loading steps were used in the calculation process for a specimen of three-dimensional circular cylinder. Computational results in the case of an uni-axial compression test for temperatures at 20oC and at 40oC were compared with available experimental measurements to verify the ability of developing numerical scheme. The isotropic response and the deviatoric response due to the thermal effect were presented from deformations in different profiles and displacement plots for the entire specimen. The characteristics of changing asphalt concrete material under a specified loading condition might be seen clearly from the numerical results, and might provide an useful information in the field of road engineering.

Key Words
temperature sensitive material; endochronic theory; finite element method; isotropic response; deviatoric response.

Address
Department of Civil Engineering, National Pingtung University of Science and Technology, Pingtung 91207, Taiwan

Abstract
Reinforced concrete buildings with shearwalls are very efficient to resist earthquake disturbances. In general, reinforced concrete frames are governed by flexure and shearwalls are governed by shear. If a structure included both frames and shearwalls, it is generally governed by shearwalls. However, the ductility of ordinary reinforced concrete is very limited. To improve the ductility, a series of tests on framed shearwalls made of corrugated steel was performed previously and the experimental results were compared with ordinary reinforced concrete frames and shearwalls. It was found that ductility of framed shearwalls could be greatly improved if the thickness of the corrugated steel wall is appropriate to the surrounding reinforced concrete frame. In this paper, an analytical model is developed to predict the horizontal load-displacement relationship of hybrid reinforced concrete frame-steel wall systems according to the analogy of truss models. This analytical model is based on equilibrium and compatibility conditions as well as constitutive laws of corrugated steel. The analytical predictions are compared with the results of tests reported in the previous paper. It is found that proposed analytical model can predict the test results with acceptable accuracy.

Key Words
hybrid system; frame-wall interaction; corrugated steel plate; constitutive model; shear wall.

Address
Department of Civil and Environmental Engineering, University of Houston, Houston, Texas, USA
Department of Civil Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan

Abstract
Characteristics of solutions of softening plasticity are discussed in this article. The localized and non-localized solutions are obtained for a three-bar truss and their stability is evaluated with the aid of the second-order work. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the second-order work exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the second-order work, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, it is proposed that the structure should follow the path corresponding to the absolute minimum point of the second-order work. The proposal is further proved equivalent to Bazant\'s path criterion derived on a thermodynamics basis.

Key Words
softening plasticity; strain localization; bifurcation; energy minimization; path criterion.

Address
Faculty of Engineering & Surveying, The University of Southern Queensland,
Toowoomba, QLD 4350, Australia

Abstract
From the equation of motion of a \"bare\" non-uniform beam (without any concentrated elements), an eigenfunction in term of four unknown integration constants can be obtained. When the last eigenfunction is substituted into the three compatible equations, one force-equilibrium equation, one governing equation for each attaching point of the concentrated element, and the boundary equations for the two ends of the beam, a matrix equation of the form [B]{C} = {0} is obtained. The solution of (where

Key Words
non-uniform beam; natural frequencies; mode shapes; bare beam; constrained beam; eigenfunction.

Address
Department of Naval Architecture and Marine Engineering, Chung Cheng Institute of Technology,
National Defense University, Yuansulin, Dashi, Taoyuan, Taiwan 335, Republic of China

Abstract
This paper presents an illustrative example of the advantages offered by inserting added viscous dampers into shear-type structures in accordance with a special scheme based upon the mass proportional damping (MPD) component of the Rayleigh viscous damping matrix. In previous works developed by the authors, it has been widely shown that, within the class of Rayleigh damped systems and under the

Key Words
added viscous dampers; concrete shear-type structure; Rayleigh damping matrix; MPD system; seismic response.

Address
Department DISTART, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy

Abstract
This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter a is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton\'s principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

Key Words
dynamic instability; non-conservativeness; sub-tangential forces; flutter and divergence; elastically restrained end.

Address
Department of Structures, University of Calabria, via Pietro Bucci, Arcavacata di Rende Cosenza, Italy
Department of Civil Engineering, DISTART, University of Bologna, Viale Risorgimento 2, Bologna, Italy

Abstract
One of the most versatile approaches for analyzing the dynamic behavior of structural systems is direct time integration of semi-discrete equations of motion. However responses computed by time integration are generally inexact and hence the corresponding errors would rather be studied in advance. In spite of the various error estimation formulations that exist in the literature, it is accepted practice to repeat the analyses with smaller time steps, followed by a comparison between the results. In this paper, after a review of this simple method and disregarding the round-off errors, a more efficient, reliable and yet simple method for estimating errors and enhancing the accuracy is proposed. The main objectives of this research are more realistic error estimation based on the concept of convergence, approximately controlling the reliability by comparing the actual rate of convergence with the integration method\'s order of accuracy, and enhancement of reliability by applying Richardson\'s extrapolation. Starting from the errors at specific time instants, the study is then generalized to cases in which the errors should be estimated and decreased at specific events e.g. peak responses. Numerical study illustrates the efficacy of the proposed method.

Key Words
direct time integration; error estimation; reliable responses; rate of convergence; Richardson\'s extrapolation; round-off error; computational cost.

Address
Civil Engineering Department, Faculty of Engineering, University of Tehran, Tehran 11365, Iran


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