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CONTENTS
Volume 36, Number 1, September10 2010
 

Abstract
A total of 28 wall panels were cast and tested under uniformly distributed axial load in oneway in-plane action to study the effect of slenderness ratio (SR) and aspect ratio (AR) on the ultimate load. Two concrete formulations, normal concrete (NC) and self compacting concrete (SCC), were used for the casting of wall panels. Out of 28 wall panels, 12 were made of NC and the remaining 16 panels were of SCC. All the 12 NC panels and 12 out of 16 SCC panels were used to study the influence of SR and the remaining 4 SCC panels were tested to study the effect of AR on the ultimate load. A brief review of studies available in literature on the strength and behaviour of reinforced concrete (RC) wall panels is presented. Load-deformation response was recorded and analyzed. The ultimate load of SCC wall panels decreases non-linearly with the increase in SR and decreases linearly with increasing values of AR. Based on this study a method is proposed to predict the ultimate load of reinforced SCC wall panels. The modified method includes the effect of SR, AR and concrete strength.

Key Words
self-compacting concrete; bearing walls; slenderness ratio; aspect ratio; one-way action; crushing; buckling.

Address
N. Ganesan:Department of Civil Engineering, National Institute of Technology Calicut, Kerala State, 673601,India
P.V. Indiraa:Department of Civil Engineering, National Institute of Technology Calicut, Kerala State, 673601,India
S. Rajendra Prasad: Department of Civil Engineering, National Institute of Technology Calicut, Kerala State, 673601, India

Abstract
The load and resistance factors are generally obtained using the First Order Reliability Method (FORM), in which the design point should be determined and derivative-based iterations have to be used. In this paper, a simple method for estimating the load and resistance factors using the first four moments of the basic random variables is proposed and a simple formula for the target mean resistance is also proposed to avoid iteration computation. Unlike the currently used method, the load and resistance factors can be determined using the proposed method even when the probability density functions (PDFs) of the basic random variables are not available. Moreover, the proposed method does not need either the iterative computation of derivatives or any design points. Thus, the present method provides a more convenient and effective way to estimate the load and resistance factors in practical engineering. Numerical examples are presented to demonstrate the advantages of the proposed fourth moment method for determining the load and resistance factors.

Key Words
load and resistance factors; fourth moment method; target mean resistance; simple formula.

Address
Zhao-Hui Lu: School of Civil Engineering and Architecture, Central South University, 22 Shaoshannan Road, Changsha 410075, China
Yan-Gang Zhao: Department of Architecture, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama 221-8686, Japan
Alfredo H-S. Ang: Department of Civil and Environmental Engineering, University of California, Irvine, E-4150 Engineering Gateway, Irvine, CA 92697-2175, USA

Abstract
For large-scale structures, the calculation of the eigensolution and the eigensensitivity is usually very time-consuming. This paper develops the Kron\'s substructuring method to compute the firstorder derivatives of the eigenvalues and eigenvectors with respect to the structural parameters. The global structure is divided into several substructures. The eigensensitivity of the substructures are calculated via the conventional manner, and then assembled into the eigensensitivity of the global structure by performing some constraints on the derivative matrices of the substructures. With the proposed substructuring method, the eigenvalue and eigenvector derivatives with respect to an elemental parameter are computed within the substructure solely which contains the element, while the derivative matrices of all other substructures with respect to the parameter are zero. Consequently this can reduce the computation cost significantly. The proposed substructuring method is applied to the GARTEUR AG-11 frame and a highway bridge, which is proved to be computationally efficient and accurate for calculation of the eigensensitivity. The influence of the master modes and the division formations are also discussed.

Key Words
substructuring method; eigensolution; eigensensitivity; model updating.

Address
Yong Xia: Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Shun Weng: Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
You-Lin Xu: Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Hong-Ping Zhu: School of Civil Engineering & Mechanics, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China

Abstract
A novel flexibility-based 1D element that captures the material nonlinearity and second order P- effects within a reinforced concrete frame member is developed. The formulation is developed for 2D planar frames in the modified fiber element framework but can readily be extended to 3D cases. The nonlinear behavior of concrete including cracking and crushing is taken into account through a modified hypo-elastic model. A parabolic and a constant shear stress distribution are used at section level to couple the normal and tangential tractions at material level. The lack of objectivity due to softening of concrete is addressed and objectivity of the response at the material level is attained by using a technique derived from the crack band approach. Finally the efficiency and accuracy of the formulation is compared with experimental results and is demonstrated by some numerical examples.

Key Words
flexibility; framed structures; objectivity; P- effects; reinforced concrete; shear.

Address
Hamid R. Valipour: School of Civil and Environmental Engineering, University of Technology, Sydney, NSW 2007, Australia
Stephen J. Foster: School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW 2052, Australia

Abstract
This study shows how uncertainties of data like material properties quantitatively have an influence on structural topology optimization results for dynamic problems, here such as both optimal topology and shape. In general, the data uncertainties may result in uncertainties of structural behaviors like deflection or stress in structural analyses. Therefore optimization solutions naturally depend on the uncertainties in structural behaviors, since structural behaviors estimated by the structural analysis method like FEM need to execute optimization procedures. In order to quantitatively estimate the effect of data uncertainties on topology optimization solutions of dynamic problems, a so-called interval analysis is utilized in this study, and it is a well-known non-stochastic approach for uncertainty estimate. Topology optimization is realized by using a typical SIMP method, and for dynamic problems the optimization seeks to maximize the first-order eigenfrequency subject to a given material limit like a volume. Numerical applications topologically optimizing dynamic wall structures with varied supports are studied to verify the non-stochastic interval analysis is also suitable to estimate topology optimization results with dynamic problems.

Key Words
topology optimization design; uncertainty; dynamic problem; eigenfrequency.

Address
Dong-Kyu Lee: Architecture & Offshore Research Department, Steel Structure Research Division, Research Institute of Industrial Science and Technology (RIST), Republic of Korea
Uwe Starossek: Structural Analysis and Steel Structures Institute, Hamburg University of Technology, Germany
Soo-Mi Shin: Research Institute of Industrial Technology, Pusan National University, Republic of Korea

Abstract
Two-dimensional elastic contact problems, including normal, tangential, and rolling contacts, are treated with the finite element method in this study. Stress boundary conditions and kinematic conditions are transformed into multiple point constraints for nodal displacements in the finite element method. Upon imposing these constraints into the finite element system equations, the calculated nodal stresses and nodal displacements satisfy stress and displacement contact conditions exactly. Frictional and frictionless contacts between elastically identical as well as elastically dissimilar materials are treated in this study. The contact lengths, sizes of slip and stick regions, the normal and the shear stresses can be found.

Key Words
contact mechanics; rolling contact; tangential contact; finite element method; multiple point constraints.

Address
C.H. Liu: Department of Mechanical and Elector-mechanical Engineering, Tamkang University, Tamsui, Taipei Shien, Taiwan, R.O.C.
I Cheng: Department of Mechanical and Elector-mechanical Engineering, Tamkang University, Tamsui, Taipei Shien, Taiwan, R.O.C.
An-Chi Tsai: Department of Mechanical and Elector-mechanical Engineering, Tamkang University, Tamsui, Taipei Shien, Taiwan, R.O.C.
Lo-Jung Wang: UL International Services Ltd.-Taiwan Branch, 1\'st Fl 260 Da-Yeh Road, Peitou, Taipei City, Taiwan, R.O.C.
J.Y. Hsu: Vivotek Inc., 6F 192 Lien-Cheng Rd., Chung-Ho, Taipei Shien, Taiwan, R.O.C.

Abstract
This paper studies the effects of spatially varying ground motions on the responses of a bridge frame located on a canyon site. Compared to the spatial ground motions on a uniform flat site, which is the usual assumptions in the analysis of spatial ground motion variation effects on structures, the spatial ground motions at different locations on surface of a canyon site have different intensities owing to local site amplifications, besides the loss of coherency and phase difference. In the proposed approach, the spatial ground motions are modelled in two steps. Firstly, the base rock motions are assumed to have the same intensity and are modelled with a filtered Tajimi-Kanai power spectral density function and an empirical spatial ground motion coherency loss function. Then, power spectral density function of ground motion on surface of the canyon site is derived by considering the site amplification effect based on the one dimensional seismic wave propagation theory. Dynamic, quasi-static and total responses of the model structure to various cases of spatially varying ground motions are estimated. For comparison, responses to uniform ground motion, to spatial ground motions without considering local site effects, to spatial ground motions without considering coherency loss or phase shift are also calculated. Discussions on the ground motion spatial variation and local soil site amplification effects on structural responses are made. In particular, the effects of neglecting the site amplifications in the analysis as adopted in most studies of spatial ground motion effect on structural responses are highlighted.

Key Words
site amplification effect; ground motion spatial variation; dynamic responses; quasi-static responses; total responses.

Address
Kaiming Bi: School of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Hong Hao: School of Civil and Resource Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Weixin Ren: Department of Civil Engineering, Central South University, Changsha 410075, China


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