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CONTENTS
Volume 9, Number 5, May 2000
 

Abstract
A comprehensive analytic study has been conducted to investigate the instability problems of metal-plate-connected (MPC) joints in light frame trusses. The primary objective in this study is to determine the governing factors that constitute the buckling of the metal connectors and their effects on the structural response of joints. Another objective is to recommend design curves for the daily structural design of these joints. The numeric data presented in this paper has emerged from a broad base that was founded on over 350 advanced computer simulations, and was supported by available experimental results obtained by others. This basic-to-applied research includes practical engineering parameters such as size of gaps, shear lengths, gauge (plate thickness) of connectors, size of un-braced areas, failure modes, and progressive disintegration of joints. Square-end members have been emphasized though the results cover the custom-made fitted joints. The results indicate that chord shears cause and dominate the buckling of MPC joints, and the shear length has a more pronounced effect than the size of gaps. Further, large gauges and small un-braced areas improve the buckling response. Several practical recommendations have been suggested throughout the paper such as keeping the ratio of gap/shear length below 3/4 for improving the buckling strength. The study reveals that multi-area joints should not be simplified as single web-to-chord MPC joints such as keeping the ratio of gap/shear length below 3/4 for improving the buckling strength, even where one web is in tension and the other in compression. Finally, the results obtained from this study favorably agree with experimental data by others, and the classic buckling theories for other structural components.

Key Words
buckling, compression, connections, connectors, critical loads, finite elements, gauge, joints, light frame, metal plate, MPC joints, shear, stability, standards, trusses, wood

Address
Hussein R, POB 744, Syracuse, NY 13210 USA

Abstract
In this paper we deal with the numerical solution of the Reissner-Mindlin plate problem with the use of high order finite elements. In previous papers we have solved the problem using approximation spaces of Serendipity type, in order to minimize the number of internal degrees of freedom. Since further numerical experiences have evidenced that the addition of bubble functions improved the quality of the results we have modified the previous family of hierarchic finite elements, adding internal degrees of freedom, to make a systematic analysis of their performance. Of course, more degrees of freedom are introduced. Nonetheless the numerical results indicate that the reduction of the error outnumbers the increase of degrees of freedom and therefore bubble plus elements are preferable.


Key Words
Reissner-Mindlin plate, conforming hierarchic finite elements, bubble functions

Address
Della Croce L, Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy
Univ Pavia, Dipartimento Matemat, I-27100 Pavia, Italy

Abstract
The natural frequencies and the corresponding mode shapes of a non-uniform beam carrying multiple point masses are determined by using the analytical-and-numerical-combined method. To confirm the reliability of the last approach, all the presented results are compared with those obtained from the existing literature or the conventional finite element method and close agreement is achieved. For a \"uniform\" beam, the natural frequencies and mode shapes of the \"clamped-hinged\" beam are exactly equal to those of the \"hinged-clamped\" beam so that one eigenvalue equation is available for two boundary conditions, but this is not true for a \"non-uniform\" beam. To improve this drawback, a simple transformation function phi(xi)=(e+xi alpha)(2) is presented. Where xi=x/L is the ratio of the axial coordinate x to the beam length L, alpha is a taper constant for the non-uniform beam, e=1.0 for \"positive\" taper and e=1.0+alpha for \"negative\" taper (where alpha is the absolute value of alpha). Based on the last function, the eigenvalue equation for a non-uniform beam with \"positive\" taper (with increasingly varying stiffness) is also available for that with \"negative\" taper (with decreasingly varying stiffness) so that half of the effort may be saved. For the purpose of comparison, the eigenvalue equations for a positively-tapered beam with five types of boundary conditions are derived. Besides, a general expression for the \"normal\" mode shapes of the non-uniform beam is also presented.

Key Words
non-uniform beam, natural frequencies, normal mode shapes, transformation function

Address
Wu JS, Natl Cheng Kung Univ, Inst Naval Architecture & Marine Engn, Tainan 701, Taiwan
Natl Cheng Kung Univ, Inst Naval Architecture & Marine Engn, Tainan 701, Taiwan

Abstract
A numerical study using nonlinear finite element analysis is performed to investigate the behavior of isolated reinforced concrete walls subjected to combined axial force and in-plane and out-of-plane bending moments. For a nonlinear finite element analysis, a computer program addressing material and geometric nonlinearities was developed. Through numerical studies, the internal force distribution in the cross-section is idealized, and then a new design method, different from the existing methods based on the plane section hypothesis was developed. According to the proposed method, variations in the interaction curve of the in-plane bending moment and axial force depends on the range of the permissible axial force per unit length, that is determined by a given amount of out-of-plane bending moment. As the out-of-plane bending moment increases, the interaction curve shrinks, indicating a decrease in the ultimate strength. The proposed method is then compared with an existing method, using the plane section hypothesis. Compared with the proposed method, the existing method overestimates the ultimate strength for the walls subjected to low out-of-plane bending moments, while it underestimates the ultimate strength for walls subject to high out-of-plane bending moments. The proposed method can address the out-of-plane local behavior of the individual wall segments that may govern the ultimate strength of the entire wall.


Key Words
biaxial bending, compression, finite element, interaction curve, plasticity, reinforced concrete wall

Address
Park H, Seoul Natl Univ, Dept Architecture, San 56-1,Shinlim Dong, Seoul 151742, South Korea
Seoul Natl Univ, Dept Architecture, Seoul 151742, South Korea

Abstract
After manufacturing a structure, the assembly of structural components is often not as perfect as expected due to the immaturity of current engineering techniques. Thus the actual buckling load for an element is sometimes not consistent with that predicted in the design. For design considerations, it is necessary to establish an analytical method for determining the buckling load experimentally. In this paper, a dynamic method is described for determining the linear buckling loads for elastic, perfectly flat plates. The proposed method does not require the application of in-plane loads and is feasible for arbitrary types of boundary conditions. It requires only the vibrational excitation of the plate. The buckling load is determined from the measured natural frequencies and vibration mode shapes.

Key Words
buckling load, natural frequency, mode shape

Address
Go CG, Natl Chung Hsing Univ, Dept Civil Engn, Taichung 40227, Taiwan
Natl Chung Hsing Univ, Dept Civil Engn, Taichung 40227, Taiwan

Abstract
A convenient method for enhancing the strength and stiffness of existing reinforced concrete beams is to bond adhesively steel plates to their tension faces. However, there is a limit to the applicability of tension face plating as the tension face plates are prone to premature debonding and, furthermore, the addition of the plate reduces the ductility of the beam. An alternative approach to tension face plating is to bond adhesively steel plates to the sides of reinforced concrete beams, as side plates are less prone to debonding and can allow the beam to remain ductile. Debonding at the ends of the side plates due to flexural forces, that is flexural peeling, is studied in this paper. A fundamental mathematical model for flexural peeling is developed, which is calibrated experimentally to produce design rules for preventing premature debonding of the plate-ends due to flexural forces. In the companion paper, the effect of shear forces on flexural peeling is quantified to produce design rules that are applied to the strengthening and stiffening of continuous reinforced concrete beams.

Key Words
retrofitting, rehabilitation, adhesive bonding, plating, reinforced concrete, flexural peeling

Address
Oehlers DJ, Univ Adelaide, Dept Civil & Environm Engn, Adelaide, SA 5050, Australia
Univ Adelaide, Dept Civil & Environm Engn, Adelaide, SA 5050, Australia
Univ New S Wales, Sch Civil Engn, Kensington, NSW 2033, Australia

Abstract
A major cause of premature debonding of tension face plates is shear peeling (Jones et al. 1988, Swamy et al. 1989, Ziraba ct al. 1994, Zhang et al. 1995), that is debonding at the plate ends that is associated with th: formation of shear diagonal cracks that are caused by the action of vertical shear forces. It is shown in this paper how side plated beams are less prone to shear peeling than tension face plated beams, as the side plate automatically increases the resistance of the reinforced concrete beam to shear peeling. Tests are used to determine the increase in the shear peeling resistance that the side plates provide, and also the effect of vertical shear forces on the pure flexural peeling strength that was determined in the companion paper. Design rules are then developed to prevent premature debonding of the plate ends due to peeling and they are applied to the strengthening and stiffening of continuous reinforced concrete beams. It is shown how these design rules for side plated beams can be adapted to allow for propped and unpropped construction and the time effects of creep and shrinkage, and how side plates can be used in conjunction with tension face plates.

Key Words
retrofitting, rehabilitation, adhesive bonding, plating, reinforced concrete, shear peeling

Address
Oehlers DJ, Univ Adelaide, Dept Civil & Environm Engn, Adelaide, SA 5050, Australia
Univ Adelaide, Dept Civil & Environm Engn, Adelaide, SA 5050, Australia
Univ New S Wales, Sch Civil Engn, Kensington, NSW 2033, Australia


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